Correction method of measurement errors, quality checking method for electronic components, and characteristic measuring system of electronic components

ABSTRACT

Actual measured results, which do not agree with a reference measuring system accurately, are corrected to the same level as results measured by the reference measuring system. An interrelating formula between results measured by an actual measuring system and results measured by a reference measuring system is obtained after measuring electrical characteristics of a correction-data acquisition sample by the reference measuring system and the actual measuring system, respectively. Then, by substituting electrical characteristics of a target electronic component measured by the actual measuring system in the interrelating formula for computation, the electric characteristics of the target electronic component is corrected to electric characteristics assumed to be obtained by the reference measuring system.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a correction method for correctingelectrical characteristics of electronic components measured by anactual measuring system with measured results, which do not agree with areference measuring system, to electrical characteristics assumed to beobtained by the reference measuring system; a quality checking methodusing the correction method for electronic components; and acharacteristic measuring system for performing the correction method onelectronic components.

2. Description of the Related Art

In measuring electrical characteristics of electronic components,sometimes, the same electronic component or the same kind thereof ismeasured by a plurality of measuring systems, such as a measuring systemset up in a site for an electronic component manufacturer and anothermeasuring system set up in a site for a user of the electroniccomponents.

Because measurement errors are different from those in each measuringsystem in such a case, the precision of measurement reproducibility islow, so that a problem arises from inconsistency of measured results forthe same electronic component or the same kind thereof.

Such measurement errors are comparatively low in the electricalcharacteristic measurement in a low frequency region, so that there isnot much problem on this point. Whereas, in a high frequency region of100 MHz or more, the measurement errors between measuring systems arelarge, so that in order to improve the precision of measurementreproducibility, calibration using an absolute correction method isperformed especially in a high frequency region of several GHz or more.

A standard device is prepared in advance in that an instrument having atarget electrical characteristic precisely identified, such as anopen/short/load/through, an example of which is the model 85052Bmanufactured by Agilent Technologies Company. Various measurements ofthis standard device by each measuring system identify the error factorof each measuring system. Then, the calibration such as a high-accuracyfull two-port correction method is performed thereon to eliminate theidentified error factor, improving the precision of measurementreproducibility (such a correction method is referred to as an absolutecorrection method below).

In such a manner, a measuring system can improve the precision ofmeasurement reproducibility by performing the high-accuracy calibrationusing the standard device mentioned above. However, such calibration canbe performed on only an electronic component with a coaxial form(referred to as a coaxial-type electronic component below) so as tomeasure precisely.

Whereas, the calibration mentioned above has been difficult to performon an electronic component with a non-coaxial form (referred to as anoncoaxial-type electronic component below). The reason thereof isdescribed below.

A standard device for noncoaxial-type electronic components is extremelydifficult to be manufactured to have substantially the same performanceas that for coaxial-type electronic components, and manufacturing costfor such a standard device becomes extremely large. Moreover, even ifthe standard device is manufactured, it is difficult to specifyelectrical characteristics thereof in high accuracy.

Furthermore, even if a standard device for noncoaxial-type electroniccomponents is prepared, in a measuring system capable of performing thehigh-accuracy calibration (such as the full two-port correction method),the standard device capable of performing the calibration mentionedabove is limited to the instrument to achieve the value (typically, theopen/short/load/through), which cannot be achieved unless the componentis of a coaxial-type. By such reasons, the calibration mentioned aboveis difficult to be performed on noncoaxial-type electronic components.

In performing a TRL correction method, a kind of calibration, a standarddevice (typically, a standard device of a through/reflection/line) fornoncoaxial-type electronic components such as waveguides and microstriplines may be easily manufactured. However, even in the standard devicesuitable for the TRL correction method, it is difficult to specifyelectrical characteristics thereof in high accuracy.

As described above, in the measurement of electrical characteristics ofnoncoaxial-type electronic components, it is difficult to improvemeasurement accuracy by performing the calibration thereon based on theabsolute correction method. Therefore, up to now, in the measurement ofelectrical characteristics of noncoaxial-type electronic components, thecalibration at junction points of the electronic component is notperformed but the measurement is performed in a state of being attachedto a measurement fixture, as will be described below.

A measurement fixture is prepared, which has coaxial input-outputterminals for a measuring system while having noncoaxial input-outputterminals for a noncoaxial-type electronic component. This measurementfixture is electrically connected to a piece of coaxial cable, which isconnected to input-output terminals of the measuring system. Then, thenoncoaxial-type electronic component is mounted on the measuring systemso that electrical characteristics of the component are measured. Inaddition, it is preferable that the calibration such as a full two-portcorrection method be performed on the coaxial cable connected to theinput-output terminals of the measuring system up to the tip end.

In such an electrical characteristic measurement method fornoncoaxial-type electronic components using the measurement fixture,calibration cannot be performed by including the measurement fixture.Therefore, the reproducibility of measured results is low. In order toincrease the reproducibility of the measured results, the followingadjustments of the measuring system are performed.

In this adjustment, one measuring system is regarded as a referencemeasuring system having a reference measurement fixture and the other isregarded as an actually measuring system having an actual measurementfixture, so that the actual measurement fixture of the actuallymeasuring system is adjusted so as to bring the measured result from theactually measuring system to that from the reference measuring system.Specifically, electrical characteristics of an arbitrary sample(electronic component) are measured by the reference measuring system;electrical characteristics of the same sample are measured by theactually measuring system, and then, the actual measurement fixture isadjusted so that both the measured results are equalized. The adjustmentis specifically performed as follows.

The actual measurement fixture is arranged that a coaxial connector tobe connected to a measuring system is attached to a printed circuitboard having input-output terminals to be connected to a sample, whichare disposed at a wiring end-portion on the substrate surface. In theactual measurement fixture structured as above, adjustment is performedas follows. While part of printed wiring on the printed circuit boardbeing cut off, or solder being put on the printed wiring, changes in themeasured results are measured, and the treatment is finalized after thesame electrical characteristics as those of the measured results in thereference measuring system are obtained.

The measuring method of electrical characteristics of electroniccomponents described above has the following problems for bothmeasurements of coaxial-type electronic components and noncoaxial-typeelectronic components.

In measuring method of coaxial-type electronic components, although thereference device necessary for the calibration is available, it isexpensive, so that there is a problem that the cost of the calibrationis increased, and by extension, the cost for measuring electricalcharacteristics of electronic components is increased.

In measuring method of noncoaxial-type electronic components, becausethe adjustment method of the actual measurement fixture mentioned aboveis not theoretically clarified but is depending on skills and hunch andtaking a lot of trouble, it is difficult to reproduce the adjustment inhigh accuracy even to the old hand.

Furthermore, such an adjustment method of the actual measurement fixtureis a method only capable of assuring the reproducibility when measuringthe sample used in the adjustment, and when another sample is measured,the reproducibility is not always assured, so that it would have to saythat the reproducibility be unstable.

SUMMARY OF THE INVENTION

Accordingly, it is a principal object of the present invention toprovide a correction method of measurement errors in that measuredresults of actual measurement, which do not perfectly agree with areference measuring system, is corrected to the same level of measuredresults by the reference measuring system.

In order to achieve the object mentioned above, a measurement-errorcorrection method, in which after electrical characteristics of a targetelectronic component are measured by an actual measuring system withmeasured results that do not agree with a reference measuring system,the measured value is corrected to electrical characteristics assumed tobe obtained by the reference measuring system, the measurement-errorcorrection method comprising the steps of preparing a correction-dataacquisition sample in advance, which generates the same electricalcharacteristics as arbitrary electrical characteristics of the targetelectronic component by measurement operation; measuring electricalcharacteristics of the correction-data acquisition sample by thereference measuring system and the actual measuring system,respectively; obtaining an interrelating formula between resultsmeasured by the reference measuring system and results measured by theactual measuring system; and correcting electrical characteristics ofthe target electronic component to electrical characteristics assumed tobe obtained by the reference measuring system by substituting theelectrical characteristics of the target electronic component measuredby the actual measuring system in the interrelating formula forcomputation. Thereby the following functions are provided.

Based on the measured results of the correction-data acquisition samplewith not-identified electrical characteristics, the interrelatingformula between the actual measuring system and the reference measuringsystem is obtained. Then, electrical characteristics of the targetelectronic component are corrected to the electrical characteristicsassumed to be obtained by the reference measuring system on the basis ofthe interrelating formula, eliminating calibration using an expensiveauthentic sample and adjustment of measurement fixtures. Moreover, theelectrical characteristic correction is performed by theoreticalcomputation, so that repeatability of electrical characteristicmeasurement of electronic components with any shapes (coaxial ornoncoaxial shape) can be increased.

The present invention proposes an analytical relative correction methodand an approximate-relative correction method as correction methodsusing the interrelating formula.

For obtaining the interrelation equation by the analytical relativecorrection method, the present invention may comprise the procedures ofcreating a theoretical equation for obtaining a measurement true valueof the actual measuring system in the signal transfer pattern and atheoretical equation for obtaining a measurement true value of thereference measuring system in the signal transfer pattern, respectively;creating the interrelating formula comprising an arithmetic expression,which includes an undetermined coefficient and directly and exclusivelyshows the relationship between the measurement true value of the actualmeasuring system and the measurement true value of the referencemeasuring system, based on both the theoretical equations; measuringelectrical characteristics of the correction-data acquisition sample bythe reference measuring system and the actual measuring system,respectively; and identifying the undetermined coefficient bysubstituting the electrical characteristics of the correction-dataacquisition sample measured by both the measuring systems in theinterrelating formula.

For obtaining the interrelation equation by the approximate-relativecorrection method, the present invention may comprise the procedures ofcreating the interrelating formula comprising an expression of degree n(n is a natural number) including an undetermined coefficient andapproximately showing the relationship between the value measured by theactual measuring system and the value measured by the referencemeasuring system, measuring electrical characteristics of thecorrection-data acquisition sample by the reference measuring system andthe actual measuring system, respectively, and identifying theundetermined coefficient by creating an undetermined-coefficientcomputing equation based on the interrelating formula so as tosubstitute the electrical characteristics of the correction-dataacquisition sample measured by both the measuring systems in theundetermined-coefficient computing equation.

Preferably, measurement-error correction is performed on a plurality ofelectrical characteristics which are included in the target electroniccomponent. In this connection, a plurality of samples having electricalcharacteristics which are different from each other as measured by themeasuring system are used as the correction-data acquisition sample.Thereby, accuracy of correction by the interrelation equation is furtherimproved. Moreover, it is enough to prepare the correction-dataacquisition samples having arbitrary electrical characteristics withoutidentifying a physical true value of the characteristics, simplifyingmanufacturing or availability.

Preferably, a characteristic of measurement-error correction is an Sparameter and a measuring instrument constituting the measuring systemis a network analyzer.

Examples of the S parameter may be a reflection coefficient in a forwarddirection, transfer coefficient in the forward direction, reflectioncoefficient in a backward direction, and transfer coefficient in thebackward direction.

Specific procedures of creating the interrelating formula by theapproximate-relative correction method are shown as follows.

The method for creating the interrelating formula comprises the stepsof:

creating the following interrelating formula (B2) comprising a linearexpression and the following undetermined coefficient computingequations (B1a) to (B1d);

preparing five correction-data acquisition samples with electricalcharacteristics, which are generated by measurement operation of themeasuring system and being different from each other, and then measuringS parameter (S₁₁ ^(n), S₂₁ ^(n), S₁₂ ^(n), and S₂₂ ^(n):n: naturalnumbers of 1 to 5) of the correction-data acquisition samples by thereference measuring system and the actual measuring system;

determining undetermined coefficients (a_(m), b_(m), c_(m), and d_(m):m; integers of 0 to 4) by substituting the measured S parameter (S₁₁^(n), S₂₁ ^(n), S₁₂ ^(n), and S₂₂ ^(n)) in the undetermined coefficientcomputing equations (B1a) to (B1d); and

inserting the identified undetermined coefficients (a_(m), b_(m), c_(m),and d_(m)) into the interrelating formula (B2). $\begin{matrix}\left\lbrack {{Numerical}\quad {Formula}\quad 1} \right\rbrack & \quad \\{\begin{pmatrix}S_{11}^{1^{*}} \\S_{11}^{2^{*}} \\S_{11}^{3^{*}} \\S_{11}^{4^{*}} \\S_{11}^{5^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & 1\end{pmatrix}\begin{pmatrix}a_{1} \\a_{2} \\a_{3} \\a_{4} \\a_{0}\end{pmatrix}}} & {B1a} \\{\begin{pmatrix}S_{21}^{1^{*}} \\S_{21}^{2^{*}} \\S_{21}^{3^{*}} \\S_{21}^{4^{*}} \\S_{21}^{5^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & 1\end{pmatrix}\begin{pmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4} \\b_{0}\end{pmatrix}}} & {B1b} \\{\begin{pmatrix}S_{12}^{1^{*}} \\S_{12}^{2^{*}} \\S_{12}^{3^{*}} \\S_{12}^{4^{*}} \\S_{12}^{5^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & 1\end{pmatrix}\begin{pmatrix}c_{1} \\c_{2} \\c_{3} \\c_{4} \\c_{0}\end{pmatrix}}} & {B1c} \\{\begin{pmatrix}S_{22}^{1^{*}} \\S_{22}^{2^{*}} \\S_{22}^{3^{*}} \\S_{22}^{4^{*}} \\S_{22}^{5^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & 1\end{pmatrix}\begin{pmatrix}d_{1} \\d_{2} \\d_{3} \\d_{4} \\d_{0}\end{pmatrix}}} & {B1d}\end{matrix}$

S₁₁ ^(n*), S₂₁ ^(n*), S₁₂ ^(n*), and S₂₂ ^(n*): the S parameter of thecorrection-data acquisition samples measured by the reference measuringsystem

S₁₁ ^(nM), S₂₁ ^(nM), S₁₂ ^(nm), and S₂₂ ^(nM): the S parameter of thecorrection-data acquisition samples measured by the actual measuringsystem $\begin{matrix}\left\lbrack {{Numerical}\quad {Formula}\quad 2} \right\rbrack & \quad \\{\begin{pmatrix}S_{11}^{*} \\S_{21}^{*} \\S_{12}^{*} \\S_{22}^{*}\end{pmatrix} = {{\begin{pmatrix}a_{1} & a_{2} & a_{3} & a_{4} \\b_{1} & b_{2} & b_{3} & b_{4} \\c_{1} & c_{2} & c_{3} & c_{4} \\d_{1} & d_{2} & d_{3} & d_{4}\end{pmatrix}\begin{pmatrix}S_{11}^{M} \\S_{21}^{M} \\S_{12}^{M} \\S_{22}^{M}\end{pmatrix}} + \begin{pmatrix}a_{0} \\b_{0} \\c_{0} \\d_{0}\end{pmatrix}}} & {B2}\end{matrix}$

S₁₁*, S₂₁*, S₁₂*, and S₂₂*: the S parameter of the target electroniccomponent assumed to be obtained by the reference measuring system

S₁₁ ^(M), S₂₁ ^(M), S₁₂ ^(M), and S₂₂ ^(M): the S parameter of thetarget electronic component measured by the actual measuring system

Other specific procedures of creating the interrelating formula by theapproximate-relative correction method are further shown as follows.

The method for creating the interrelating formula comprises the stepsof:

creating the following interrelating formulas (C2a) to (C2d) comprisinga quadratic expression and the following undetermined coefficientcomputing equations (C1a) to (C1d);

preparing 15 correction-data acquisition samples with electricalcharacteristics, which are generated by measurement operation and beingdifferent from each other, and then measuring S parameter (S₁₁ ^(p), S₂₁^(p), S₁₂ ^(p), and S₂₂ ^(p): p: natural numbers of 1 to 15) of thecorrection-data acquisition samples by the reference measuring systemand the actual measuring system;

determining undetermined coefficients (a_(q), b_(q), c_(q), and d_(q):q; integers of 0 to 14) by substituting the measured S parameter (S₁₁^(p), S₂₁ ^(p), S₁₂ ^(p), and S₂₂ ^(p)) in the undetermined coefficientcomputing equations (C1a) to (C1d); and

inserting the identified undetermined coefficients (a_(q), b_(q), c_(q),and d_(q)) into the interrelating formulas (C2a) to (C2d).$\begin{matrix}{\quad {\left\lbrack {{Numerical}\quad {Formula}\quad 3} \right\rbrack \quad {C1a}}} \\{\begin{pmatrix}S_{11}^{1^{*}} \\S_{11}^{2^{*}} \\S_{11}^{3^{*}} \\S_{11}^{4^{*}} \\S_{11}^{5^{*}} \\S_{11}^{6^{*}} \\S_{11}^{7^{*}} \\S_{11}^{8^{*}} \\S_{11}^{9^{*}} \\S_{11}^{10^{*}} \\S_{11}^{11^{*}} \\S_{11}^{12^{*}} \\S_{11}^{13^{*}} \\S_{11}^{14^{*}} \\S_{11}^{15^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & \left( S_{11}^{1M} \right)^{2} & \left( S_{21}^{1M} \right)^{2} & \left( S_{12}^{1M} \right)^{2} & \left( S_{22}^{1M} \right)^{2} & {S_{11}^{1M}S_{21}^{1M}} & {S_{11}^{1M}S_{12}^{1M}} & {S_{11}^{1M}S_{22}^{1M}} & {S_{21}^{1M}S_{12}^{1M}} & {S_{21}^{1M}S_{22}^{1M}} & {S_{12}^{1M}S_{22}^{1M}} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & \left( S_{11}^{2M} \right)^{2} & \left( S_{21}^{2M} \right)^{2} & \left( S_{12}^{2M} \right)^{2} & \left( S_{22}^{2M} \right)^{2} & {S_{11}^{2M}S_{21}^{2M}} & {S_{11}^{2M}S_{12}^{2M}} & {S_{11}^{2M}S_{22}^{2M}} & {S_{21}^{2M}S_{12}^{2M}} & {S_{21}^{2M}S_{22}^{2M}} & {S_{12}^{2M}S_{22}^{2M}} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & \left( S_{11}^{3M} \right)^{2} & \left( S_{21}^{3M} \right)^{2} & \left( S_{12}^{3M} \right)^{2} & \left( S_{22}^{3M} \right)^{2} & {S_{11}^{3M}S_{21}^{3M}} & {S_{11}^{3M}S_{12}^{3M}} & {S_{11}^{3M}S_{22}^{3M}} & {S_{21}^{3M}S_{12}^{3M}} & {S_{21}^{3M}S_{22}^{3M}} & {S_{12}^{3M}S_{22}^{3M}} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & \left( S_{11}^{4M} \right)^{2} & \left( S_{21}^{4M} \right)^{2} & \left( S_{12}^{4M} \right)^{2} & \left( S_{22}^{4M} \right)^{2} & {S_{11}^{4M}S_{21}^{4M}} & {S_{11}^{4M}S_{12}^{4M}} & {S_{11}^{4M}S_{22}^{4M}} & {S_{21}^{4M}S_{12}^{4M}} & {S_{21}^{4M}S_{22}^{4M}} & {S_{12}^{4M}S_{22}^{4M}} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & \left( S_{11}^{5M} \right)^{2} & \left( S_{21}^{5M} \right)^{2} & \left( S_{12}^{5M} \right)^{2} & \left( S_{22}^{5M} \right)^{2} & {S_{11}^{5M}S_{21}^{5M}} & {S_{11}^{5M}S_{12}^{5M}} & {S_{11}^{5M}S_{22}^{5M}} & {S_{21}^{5M}S_{12}^{5M}} & {S_{21}^{5M}S_{22}^{5M}} & {S_{12}^{5M}S_{22}^{5M}} & 1 \\S_{11}^{6M} & S_{21}^{6M} & S_{12}^{6M} & S_{22}^{6M} & \left( S_{11}^{6M} \right)^{2} & \left( S_{21}^{6M} \right)^{2} & \left( S_{12}^{6M} \right)^{2} & \left( S_{22}^{6M} \right)^{2} & {S_{11}^{6M}S_{21}^{6M}} & {S_{11}^{6M}S_{12}^{6M}} & {S_{11}^{6M}S_{22}^{6M}} & {S_{21}^{6M}S_{12}^{6M}} & {S_{21}^{6M}S_{22}^{6M}} & {S_{12}^{6M}S_{22}^{6M}} & 1 \\S_{11}^{7M} & S_{21}^{7M} & S_{12}^{7M} & S_{22}^{7M} & \left( S_{11}^{7M} \right)^{2} & \left( S_{21}^{7M} \right)^{2} & \left( S_{12}^{7M} \right)^{2} & \left( S_{22}^{7M} \right)^{2} & {S_{11}^{7M}S_{21}^{7M}} & {S_{11}^{7M}S_{12}^{7M}} & {S_{11}^{7M}S_{22}^{7M}} & {S_{21}^{7M}S_{12}^{7M}} & {S_{21}^{7M}S_{22}^{7M}} & {S_{12}^{7M}S_{22}^{7M}} & 1 \\S_{11}^{8M} & S_{21}^{8M} & S_{12}^{8M} & S_{22}^{8M} & \left( S_{11}^{8M} \right)^{2} & \left( S_{21}^{8M} \right)^{2} & \left( S_{12}^{8M} \right)^{2} & \left( S_{22}^{8M} \right)^{2} & {S_{11}^{8M}S_{21}^{8M}} & {S_{11}^{8M}S_{12}^{8M}} & {S_{11}^{8M}S_{22}^{8M}} & {S_{21}^{8M}S_{12}^{8M}} & {S_{21}^{8M}S_{22}^{8M}} & {S_{12}^{8M}S_{22}^{8M}} & 1 \\S_{11}^{9M} & S_{21}^{9M} & S_{12}^{9M} & S_{22}^{9M} & \left( S_{11}^{9M} \right)^{2} & \left( S_{21}^{9M} \right)^{2} & \left( S_{12}^{9M} \right)^{2} & \left( S_{22}^{9M} \right)^{2} & {S_{11}^{9M}S_{21}^{9M}} & {S_{11}^{9M}S_{12}^{9M}} & {S_{11}^{9M}S_{22}^{9M}} & {S_{21}^{9M}S_{12}^{9M}} & {S_{21}^{9M}S_{22}^{9M}} & {S_{12}^{9M}S_{22}^{9M}} & 1 \\S_{11}^{10M} & S_{21}^{10M} & S_{12}^{10M} & S_{22}^{10M} & \left( S_{11}^{10M} \right)^{2} & \left( S_{21}^{10M} \right)^{2} & \left( S_{12}^{10M} \right)^{2} & \left( S_{22}^{10M} \right)^{2} & {S_{11}^{10M}S_{21}^{10M}} & {S_{11}^{10M}S_{12}^{10M}} & {S_{11}^{10M}S_{22}^{10M}} & {S_{21}^{10M}S_{12}^{10M}} & {S_{21}^{10M}S_{22}^{10M}} & {S_{12}^{10M}S_{22}^{10M}} & 1 \\S_{11}^{11M} & S_{21}^{11M} & S_{12}^{11M} & S_{22}^{11M} & \left( S_{11}^{11M} \right)^{2} & \left( S_{21}^{11M} \right)^{2} & \left( S_{12}^{11M} \right)^{2} & \left( S_{22}^{11M} \right)^{2} & {S_{11}^{11M}S_{21}^{11M}} & {S_{11}^{11M}S_{12}^{11M}} & {S_{11}^{11M}S_{22}^{11M}} & {S_{21}^{11M}S_{12}^{11M}} & {S_{21}^{11M}S_{22}^{11M}} & {S_{12}^{11M}S_{22}^{11M}} & 1 \\S_{11}^{12M} & S_{21}^{12M} & S_{12}^{12M} & S_{22}^{12M} & \left( S_{11}^{12M} \right)^{2} & \left( S_{21}^{12M} \right)^{2} & \left( S_{12}^{12M} \right)^{2} & \left( S_{22}^{12M} \right)^{2} & {S_{11}^{12M}S_{21}^{12M}} & {S_{11}^{12M}S_{12}^{12M}} & {S_{11}^{12M}S_{22}^{12M}} & {S_{21}^{12M}S_{12}^{12M}} & {S_{21}^{12M}S_{22}^{12M}} & {S_{12}^{12M}S_{22}^{12M}} & 1 \\S_{11}^{13M} & S_{21}^{13M} & S_{12}^{13M} & S_{22}^{13M} & \left( S_{11}^{13M} \right)^{2} & \left( S_{21}^{13M} \right)^{2} & \left( S_{12}^{13M} \right)^{2} & \left( S_{22}^{13M} \right)^{2} & {S_{11}^{13M}S_{21}^{13M}} & {S_{11}^{13M}S_{12}^{13M}} & {S_{11}^{13M}S_{22}^{13M}} & {S_{21}^{13M}S_{12}^{13M}} & {S_{21}^{13M}S_{22}^{13M}} & {S_{12}^{13M}S_{22}^{13M}} & 1 \\S_{11}^{14M} & S_{21}^{14M} & S_{12}^{14M} & S_{22}^{14M} & \left( S_{11}^{14M} \right)^{2} & \left( S_{21}^{14M} \right)^{2} & \left( S_{12}^{14M} \right)^{2} & \left( S_{22}^{14M} \right)^{2} & {S_{11}^{14M}S_{21}^{14M}} & {S_{11}^{14M}S_{12}^{14M}} & {S_{11}^{14M}S_{22}^{14M}} & {S_{21}^{14M}S_{12}^{14M}} & {S_{21}^{14M}S_{22}^{14M}} & {S_{12}^{14M}S_{22}^{14M}} & 1 \\S_{11}^{15M} & S_{21}^{15M} & S_{12}^{15M} & S_{22}^{15M} & \left( S_{11}^{15M} \right)^{2} & \left( S_{21}^{15M} \right)^{2} & \left( S_{12}^{15M} \right)^{2} & \left( S_{22}^{15M} \right)^{2} & {S_{11}^{15M}S_{21}^{15M}} & {S_{11}^{15M}S_{12}^{15M}} & {S_{11}^{15M}S_{22}^{15M}} & {S_{21}^{15M}S_{12}^{15M}} & {S_{21}^{15M}S_{22}^{15M}} & {S_{12}^{15M}S_{22}^{15M}} & 1\end{pmatrix}\begin{pmatrix}a_{1} \\a_{2} \\a_{3} \\a_{4} \\a_{5} \\a_{6} \\a_{7} \\a_{8} \\a_{9} \\a_{10} \\a_{11} \\a_{12} \\a_{13} \\a_{14} \\a_{0}\end{pmatrix}}} \\{\left\lbrack {{Numerical}\quad {Formula}\quad 4} \right\rbrack \quad {C1b}} \\{\begin{pmatrix}S_{21}^{1^{*}} \\S_{21}^{2^{*}} \\S_{21}^{3^{*}} \\S_{21}^{4^{*}} \\S_{21}^{5^{*}} \\S_{21}^{6^{*}} \\S_{21}^{7^{*}} \\S_{21}^{8^{*}} \\S_{21}^{9^{*}} \\S_{21}^{10^{*}} \\S_{21}^{11^{*}} \\S_{21}^{12^{*}} \\S_{21}^{13^{*}} \\S_{21}^{14^{*}} \\S_{21}^{15^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & \left( S_{11}^{1M} \right)^{2} & \left( S_{21}^{1M} \right)^{2} & \left( S_{12}^{1M} \right)^{2} & \left( S_{22}^{1M} \right)^{2} & {S_{11}^{1M}S_{21}^{1M}} & {S_{11}^{1M}S_{12}^{1M}} & {S_{11}^{1M}S_{22}^{1M}} & {S_{21}^{1M}S_{12}^{1M}} & {S_{21}^{1M}S_{22}^{1M}} & {S_{12}^{1M}S_{22}^{1M}} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & \left( S_{11}^{2M} \right)^{2} & \left( S_{21}^{2M} \right)^{2} & \left( S_{12}^{2M} \right)^{2} & \left( S_{22}^{2M} \right)^{2} & {S_{11}^{2M}S_{21}^{2M}} & {S_{11}^{2M}S_{12}^{2M}} & {S_{11}^{2M}S_{22}^{2M}} & {S_{21}^{2M}S_{12}^{2M}} & {S_{21}^{2M}S_{22}^{2M}} & {S_{12}^{2M}S_{22}^{2M}} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & \left( S_{11}^{3M} \right)^{2} & \left( S_{21}^{3M} \right)^{2} & \left( S_{12}^{3M} \right)^{2} & \left( S_{22}^{3M} \right)^{2} & {S_{11}^{3M}S_{21}^{3M}} & {S_{11}^{3M}S_{12}^{3M}} & {S_{11}^{3M}S_{22}^{3M}} & {S_{21}^{3M}S_{12}^{3M}} & {S_{21}^{3M}S_{22}^{3M}} & {S_{12}^{3M}S_{22}^{3M}} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & \left( S_{11}^{4M} \right)^{2} & \left( S_{21}^{4M} \right)^{2} & \left( S_{12}^{4M} \right)^{2} & \left( S_{22}^{4M} \right)^{2} & {S_{11}^{4M}S_{21}^{4M}} & {S_{11}^{4M}S_{12}^{4M}} & {S_{11}^{4M}S_{22}^{4M}} & {S_{21}^{4M}S_{12}^{4M}} & {S_{21}^{4M}S_{22}^{4M}} & {S_{12}^{4M}S_{22}^{4M}} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & \left( S_{11}^{5M} \right)^{2} & \left( S_{21}^{5M} \right)^{2} & \left( S_{12}^{5M} \right)^{2} & \left( S_{22}^{5M} \right)^{2} & {S_{11}^{5M}S_{21}^{5M}} & {S_{11}^{5M}S_{12}^{5M}} & {S_{11}^{5M}S_{22}^{5M}} & {S_{21}^{5M}S_{12}^{5M}} & {S_{21}^{5M}S_{22}^{5M}} & {S_{12}^{5M}S_{22}^{5M}} & 1 \\S_{11}^{6M} & S_{21}^{6M} & S_{12}^{6M} & S_{22}^{6M} & \left( S_{11}^{6M} \right)^{2} & \left( S_{21}^{6M} \right)^{2} & \left( S_{12}^{6M} \right)^{2} & \left( S_{22}^{6M} \right)^{2} & {S_{11}^{6M}S_{21}^{6M}} & {S_{11}^{6M}S_{12}^{6M}} & {S_{11}^{6M}S_{22}^{6M}} & {S_{21}^{6M}S_{12}^{6M}} & {S_{21}^{6M}S_{22}^{6M}} & {S_{12}^{6M}S_{22}^{6M}} & 1 \\S_{11}^{7M} & S_{21}^{7M} & S_{12}^{7M} & S_{22}^{7M} & \left( S_{11}^{7M} \right)^{2} & \left( S_{21}^{7M} \right)^{2} & \left( S_{12}^{7M} \right)^{2} & \left( S_{22}^{7M} \right)^{2} & {S_{11}^{7M}S_{21}^{7M}} & {S_{11}^{7M}S_{12}^{7M}} & {S_{11}^{7M}S_{22}^{7M}} & {S_{21}^{7M}S_{12}^{7M}} & {S_{21}^{7M}S_{22}^{7M}} & {S_{12}^{7M}S_{22}^{7M}} & 1 \\S_{11}^{8M} & S_{21}^{8M} & S_{12}^{8M} & S_{22}^{8M} & \left( S_{11}^{8M} \right)^{2} & \left( S_{21}^{8M} \right)^{2} & \left( S_{12}^{8M} \right)^{2} & \left( S_{22}^{8M} \right)^{2} & {S_{11}^{8M}S_{21}^{8M}} & {S_{11}^{8M}S_{12}^{8M}} & {S_{11}^{8M}S_{22}^{8M}} & {S_{21}^{8M}S_{12}^{8M}} & {S_{21}^{8M}S_{22}^{8M}} & {S_{12}^{8M}S_{22}^{8M}} & 1 \\S_{11}^{9M} & S_{21}^{9M} & S_{12}^{9M} & S_{22}^{9M} & \left( S_{11}^{9M} \right)^{2} & \left( S_{21}^{9M} \right)^{2} & \left( S_{12}^{9M} \right)^{2} & \left( S_{22}^{9M} \right)^{2} & {S_{11}^{9M}S_{21}^{9M}} & {S_{11}^{9M}S_{12}^{9M}} & {S_{11}^{9M}S_{22}^{9M}} & {S_{21}^{9M}S_{12}^{9M}} & {S_{21}^{9M}S_{22}^{9M}} & {S_{12}^{9M}S_{22}^{9M}} & 1 \\S_{11}^{10M} & S_{21}^{10M} & S_{12}^{10M} & S_{22}^{10M} & \left( S_{11}^{10M} \right)^{2} & \left( S_{21}^{10M} \right)^{2} & \left( S_{12}^{10M} \right)^{2} & \left( S_{22}^{10M} \right)^{2} & {S_{11}^{10M}S_{21}^{10M}} & {S_{11}^{10M}S_{12}^{10M}} & {S_{11}^{10M}S_{22}^{10M}} & {S_{21}^{10M}S_{12}^{10M}} & {S_{21}^{10M}S_{22}^{10M}} & {S_{12}^{10M}S_{22}^{10M}} & 1 \\S_{11}^{11M} & S_{21}^{11M} & S_{12}^{11M} & S_{22}^{11M} & \left( S_{11}^{11M} \right)^{2} & \left( S_{21}^{11M} \right)^{2} & \left( S_{12}^{11M} \right)^{2} & \left( S_{22}^{11M} \right)^{2} & {S_{11}^{11M}S_{21}^{11M}} & {S_{11}^{11M}S_{12}^{11M}} & {S_{11}^{11M}S_{22}^{11M}} & {S_{21}^{11M}S_{12}^{11M}} & {S_{21}^{11M}S_{22}^{11M}} & {S_{12}^{11M}S_{22}^{11M}} & 1 \\S_{11}^{12M} & S_{21}^{12M} & S_{12}^{12M} & S_{22}^{12M} & \left( S_{11}^{12M} \right)^{2} & \left( S_{21}^{12M} \right)^{2} & \left( S_{12}^{12M} \right)^{2} & \left( S_{22}^{12M} \right)^{2} & {S_{11}^{12M}S_{21}^{12M}} & {S_{11}^{12M}S_{12}^{12M}} & {S_{11}^{12M}S_{22}^{12M}} & {S_{21}^{12M}S_{12}^{12M}} & {S_{21}^{12M}S_{22}^{12M}} & {S_{12}^{12M}S_{22}^{12M}} & 1 \\S_{11}^{13M} & S_{21}^{13M} & S_{12}^{13M} & S_{22}^{13M} & \left( S_{11}^{13M} \right)^{2} & \left( S_{21}^{13M} \right)^{2} & \left( S_{12}^{13M} \right)^{2} & \left( S_{22}^{13M} \right)^{2} & {S_{11}^{13M}S_{21}^{13M}} & {S_{11}^{13M}S_{12}^{13M}} & {S_{11}^{13M}S_{22}^{13M}} & {S_{21}^{13M}S_{12}^{13M}} & {S_{21}^{13M}S_{22}^{13M}} & {S_{12}^{13M}S_{22}^{13M}} & 1 \\S_{11}^{14M} & S_{21}^{14M} & S_{12}^{14M} & S_{22}^{14M} & \left( S_{11}^{14M} \right)^{2} & \left( S_{21}^{14M} \right)^{2} & \left( S_{12}^{14M} \right)^{2} & \left( S_{22}^{14M} \right)^{2} & {S_{11}^{14M}S_{21}^{14M}} & {S_{11}^{14M}S_{12}^{14M}} & {S_{11}^{14M}S_{22}^{14M}} & {S_{21}^{14M}S_{12}^{14M}} & {S_{21}^{14M}S_{22}^{14M}} & {S_{12}^{14M}S_{22}^{14M}} & 1 \\S_{11}^{15M} & S_{21}^{15M} & S_{12}^{15M} & S_{22}^{15M} & \left( S_{11}^{15M} \right)^{2} & \left( S_{21}^{15M} \right)^{2} & \left( S_{12}^{15M} \right)^{2} & \left( S_{22}^{15M} \right)^{2} & {S_{11}^{15M}S_{21}^{15M}} & {S_{11}^{15M}S_{12}^{15M}} & {S_{11}^{15M}S_{22}^{15M}} & {S_{21}^{15M}S_{12}^{15M}} & {S_{21}^{15M}S_{22}^{15M}} & {S_{12}^{15M}S_{22}^{15M}} & 1\end{pmatrix}\begin{pmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4} \\b_{5} \\b_{6} \\b_{7} \\b_{8} \\b_{9} \\b_{10} \\b_{11} \\b_{12} \\b_{13} \\b_{14} \\b_{0}\end{pmatrix}}} \\{\left\lbrack {{Numerical}\quad {Formula}\quad 5} \right\rbrack \quad {C1c}} \\{\begin{pmatrix}S_{12}^{1^{*}} \\S_{12}^{2^{*}} \\S_{12}^{3^{*}} \\S_{12}^{4^{*}} \\S_{12}^{5^{*}} \\S_{12}^{6^{*}} \\S_{12}^{7^{*}} \\S_{12}^{8^{*}} \\S_{12}^{9^{*}} \\S_{12}^{10^{*}} \\S_{12}^{11^{*}} \\S_{12}^{12^{*}} \\S_{12}^{13^{*}} \\S_{12}^{14^{*}} \\S_{12}^{15^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & \left( S_{11}^{1M} \right)^{2} & \left( S_{21}^{1M} \right)^{2} & \left( S_{12}^{1M} \right)^{2} & \left( S_{22}^{1M} \right)^{2} & {S_{11}^{1M}S_{21}^{1M}} & {S_{11}^{1M}S_{12}^{1M}} & {S_{11}^{1M}S_{22}^{1M}} & {S_{21}^{1M}S_{12}^{1M}} & {S_{21}^{1M}S_{22}^{1M}} & {S_{12}^{1M}S_{22}^{1M}} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & \left( S_{11}^{2M} \right)^{2} & \left( S_{21}^{2M} \right)^{2} & \left( S_{12}^{2M} \right)^{2} & \left( S_{22}^{2M} \right)^{2} & {S_{11}^{2M}S_{21}^{2M}} & {S_{11}^{2M}S_{12}^{2M}} & {S_{11}^{2M}S_{22}^{2M}} & {S_{21}^{2M}S_{12}^{2M}} & {S_{21}^{2M}S_{22}^{2M}} & {S_{12}^{2M}S_{22}^{2M}} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & \left( S_{11}^{3M} \right)^{2} & \left( S_{21}^{3M} \right)^{2} & \left( S_{12}^{3M} \right)^{2} & \left( S_{22}^{3M} \right)^{2} & {S_{11}^{3M}S_{21}^{3M}} & {S_{11}^{3M}S_{12}^{3M}} & {S_{11}^{3M}S_{22}^{3M}} & {S_{21}^{3M}S_{12}^{3M}} & {S_{21}^{3M}S_{22}^{3M}} & {S_{12}^{3M}S_{22}^{3M}} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & \left( S_{11}^{4M} \right)^{2} & \left( S_{21}^{4M} \right)^{2} & \left( S_{12}^{4M} \right)^{2} & \left( S_{22}^{4M} \right)^{2} & {S_{11}^{4M}S_{21}^{4M}} & {S_{11}^{4M}S_{12}^{4M}} & {S_{11}^{4M}S_{22}^{4M}} & {S_{21}^{4M}S_{12}^{4M}} & {S_{21}^{4M}S_{22}^{4M}} & {S_{12}^{4M}S_{22}^{4M}} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & \left( S_{11}^{5M} \right)^{2} & \left( S_{21}^{5M} \right)^{2} & \left( S_{12}^{5M} \right)^{2} & \left( S_{22}^{5M} \right)^{2} & {S_{11}^{5M}S_{21}^{5M}} & {S_{11}^{5M}S_{12}^{5M}} & {S_{11}^{5M}S_{22}^{5M}} & {S_{21}^{5M}S_{12}^{5M}} & {S_{21}^{5M}S_{22}^{5M}} & {S_{12}^{5M}S_{22}^{5M}} & 1 \\S_{11}^{6M} & S_{21}^{6M} & S_{12}^{6M} & S_{22}^{6M} & \left( S_{11}^{6M} \right)^{2} & \left( S_{21}^{6M} \right)^{2} & \left( S_{12}^{6M} \right)^{2} & \left( S_{22}^{6M} \right)^{2} & {S_{11}^{6M}S_{21}^{6M}} & {S_{11}^{6M}S_{12}^{6M}} & {S_{11}^{6M}S_{22}^{6M}} & {S_{21}^{6M}S_{12}^{6M}} & {S_{21}^{6M}S_{22}^{6M}} & {S_{12}^{6M}S_{22}^{6M}} & 1 \\S_{11}^{7M} & S_{21}^{7M} & S_{12}^{7M} & S_{22}^{7M} & \left( S_{11}^{7M} \right)^{2} & \left( S_{21}^{7M} \right)^{2} & \left( S_{12}^{7M} \right)^{2} & \left( S_{22}^{7M} \right)^{2} & {S_{11}^{7M}S_{21}^{7M}} & {S_{11}^{7M}S_{12}^{7M}} & {S_{11}^{7M}S_{22}^{7M}} & {S_{21}^{7M}S_{12}^{7M}} & {S_{21}^{7M}S_{22}^{7M}} & {S_{12}^{7M}S_{22}^{7M}} & 1 \\S_{11}^{8M} & S_{21}^{8M} & S_{12}^{8M} & S_{22}^{8M} & \left( S_{11}^{8M} \right)^{2} & \left( S_{21}^{8M} \right)^{2} & \left( S_{12}^{8M} \right)^{2} & \left( S_{22}^{8M} \right)^{2} & {S_{11}^{8M}S_{21}^{8M}} & {S_{11}^{8M}S_{12}^{8M}} & {S_{11}^{8M}S_{22}^{8M}} & {S_{21}^{8M}S_{12}^{8M}} & {S_{21}^{8M}S_{22}^{8M}} & {S_{12}^{8M}S_{22}^{8M}} & 1 \\S_{11}^{9M} & S_{21}^{9M} & S_{12}^{9M} & S_{22}^{9M} & \left( S_{11}^{9M} \right)^{2} & \left( S_{21}^{9M} \right)^{2} & \left( S_{12}^{9M} \right)^{2} & \left( S_{22}^{9M} \right)^{2} & {S_{11}^{9M}S_{21}^{9M}} & {S_{11}^{9M}S_{12}^{9M}} & {S_{11}^{9M}S_{22}^{9M}} & {S_{21}^{9M}S_{12}^{9M}} & {S_{21}^{9M}S_{22}^{9M}} & {S_{12}^{9M}S_{22}^{9M}} & 1 \\S_{11}^{10M} & S_{21}^{10M} & S_{12}^{10M} & S_{22}^{10M} & \left( S_{11}^{10M} \right)^{2} & \left( S_{21}^{10M} \right)^{2} & \left( S_{12}^{10M} \right)^{2} & \left( S_{22}^{10M} \right)^{2} & {S_{11}^{10M}S_{21}^{10M}} & {S_{11}^{10M}S_{12}^{10M}} & {S_{11}^{10M}S_{22}^{10M}} & {S_{21}^{10M}S_{12}^{10M}} & {S_{21}^{10M}S_{22}^{10M}} & {S_{12}^{10M}S_{22}^{10M}} & 1 \\S_{11}^{11M} & S_{21}^{11M} & S_{12}^{11M} & S_{22}^{11M} & \left( S_{11}^{11M} \right)^{2} & \left( S_{21}^{11M} \right)^{2} & \left( S_{12}^{11M} \right)^{2} & \left( S_{22}^{11M} \right)^{2} & {S_{11}^{11M}S_{21}^{11M}} & {S_{11}^{11M}S_{12}^{11M}} & {S_{11}^{11M}S_{22}^{11M}} & {S_{21}^{11M}S_{12}^{11M}} & {S_{21}^{11M}S_{22}^{11M}} & {S_{12}^{11M}S_{22}^{11M}} & 1 \\S_{11}^{12M} & S_{21}^{12M} & S_{12}^{12M} & S_{22}^{12M} & \left( S_{11}^{12M} \right)^{2} & \left( S_{21}^{12M} \right)^{2} & \left( S_{12}^{12M} \right)^{2} & \left( S_{22}^{12M} \right)^{2} & {S_{11}^{12M}S_{21}^{12M}} & {S_{11}^{12M}S_{12}^{12M}} & {S_{11}^{12M}S_{22}^{12M}} & {S_{21}^{12M}S_{12}^{12M}} & {S_{21}^{12M}S_{22}^{12M}} & {S_{12}^{12M}S_{22}^{12M}} & 1 \\S_{11}^{13M} & S_{21}^{13M} & S_{12}^{13M} & S_{22}^{13M} & \left( S_{11}^{13M} \right)^{2} & \left( S_{21}^{13M} \right)^{2} & \left( S_{12}^{13M} \right)^{2} & \left( S_{22}^{13M} \right)^{2} & {S_{11}^{13M}S_{21}^{13M}} & {S_{11}^{13M}S_{12}^{13M}} & {S_{11}^{13M}S_{22}^{13M}} & {S_{21}^{13M}S_{12}^{13M}} & {S_{21}^{13M}S_{22}^{13M}} & {S_{12}^{13M}S_{22}^{13M}} & 1 \\S_{11}^{14M} & S_{21}^{14M} & S_{12}^{14M} & S_{22}^{14M} & \left( S_{11}^{14M} \right)^{2} & \left( S_{21}^{14M} \right)^{2} & \left( S_{12}^{14M} \right)^{2} & \left( S_{22}^{14M} \right)^{2} & {S_{11}^{14M}S_{21}^{14M}} & {S_{11}^{14M}S_{12}^{14M}} & {S_{11}^{14M}S_{22}^{14M}} & {S_{21}^{14M}S_{12}^{14M}} & {S_{21}^{14M}S_{22}^{14M}} & {S_{12}^{14M}S_{22}^{14M}} & 1 \\S_{11}^{15M} & S_{21}^{15M} & S_{12}^{15M} & S_{22}^{15M} & \left( S_{11}^{15M} \right)^{2} & \left( S_{21}^{15M} \right)^{2} & \left( S_{12}^{15M} \right)^{2} & \left( S_{22}^{15M} \right)^{2} & {S_{11}^{15M}S_{21}^{15M}} & {S_{11}^{15M}S_{12}^{15M}} & {S_{11}^{15M}S_{22}^{15M}} & {S_{21}^{15M}S_{12}^{15M}} & {S_{21}^{15M}S_{22}^{15M}} & {S_{12}^{15M}S_{22}^{15M}} & 1\end{pmatrix}\begin{pmatrix}c_{1} \\c_{2} \\c_{3} \\c_{4} \\c_{5} \\c_{6} \\c_{7} \\c_{8} \\c_{9} \\c_{10} \\c_{11} \\c_{12} \\c_{13} \\c_{14} \\c_{0}\end{pmatrix}}} \\{\left\lbrack {{Numerical}\quad {Formula}\quad 6} \right\rbrack \quad {C1d}} \\{\begin{pmatrix}S_{22}^{1^{*}} \\S_{22}^{2^{*}} \\S_{22}^{3^{*}} \\S_{22}^{4^{*}} \\S_{22}^{5^{*}} \\S_{22}^{6^{*}} \\S_{22}^{7^{*}} \\S_{22}^{8^{*}} \\S_{22}^{9^{*}} \\S_{22}^{10^{*}} \\S_{22}^{11^{*}} \\S_{22}^{12^{*}} \\S_{22}^{13^{*}} \\S_{22}^{14^{*}} \\S_{22}^{15^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & \left( S_{11}^{1M} \right)^{2} & \left( S_{21}^{1M} \right)^{2} & \left( S_{12}^{1M} \right)^{2} & \left( S_{22}^{1M} \right)^{2} & {S_{11}^{1M}S_{21}^{1M}} & {S_{11}^{1M}S_{12}^{1M}} & {S_{11}^{1M}S_{22}^{1M}} & {S_{21}^{1M}S_{12}^{1M}} & {S_{21}^{1M}S_{22}^{1M}} & {S_{12}^{1M}S_{22}^{1M}} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & \left( S_{11}^{2M} \right)^{2} & \left( S_{21}^{2M} \right)^{2} & \left( S_{12}^{2M} \right)^{2} & \left( S_{22}^{2M} \right)^{2} & {S_{11}^{2M}S_{21}^{2M}} & {S_{11}^{2M}S_{12}^{2M}} & {S_{11}^{2M}S_{22}^{2M}} & {S_{21}^{2M}S_{12}^{2M}} & {S_{21}^{2M}S_{22}^{2M}} & {S_{12}^{2M}S_{22}^{2M}} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & \left( S_{11}^{3M} \right)^{2} & \left( S_{21}^{3M} \right)^{2} & \left( S_{12}^{3M} \right)^{2} & \left( S_{22}^{3M} \right)^{2} & {S_{11}^{3M}S_{21}^{3M}} & {S_{11}^{3M}S_{12}^{3M}} & {S_{11}^{3M}S_{22}^{3M}} & {S_{21}^{3M}S_{12}^{3M}} & {S_{21}^{3M}S_{22}^{3M}} & {S_{12}^{3M}S_{22}^{3M}} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & \left( S_{11}^{4M} \right)^{2} & \left( S_{21}^{4M} \right)^{2} & \left( S_{12}^{4M} \right)^{2} & \left( S_{22}^{4M} \right)^{2} & {S_{11}^{4M}S_{21}^{4M}} & {S_{11}^{4M}S_{12}^{4M}} & {S_{11}^{4M}S_{22}^{4M}} & {S_{21}^{4M}S_{12}^{4M}} & {S_{21}^{4M}S_{22}^{4M}} & {S_{12}^{4M}S_{22}^{4M}} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & \left( S_{11}^{5M} \right)^{2} & \left( S_{21}^{5M} \right)^{2} & \left( S_{12}^{5M} \right)^{2} & \left( S_{22}^{5M} \right)^{2} & {S_{11}^{5M}S_{21}^{5M}} & {S_{11}^{5M}S_{12}^{5M}} & {S_{11}^{5M}S_{22}^{5M}} & {S_{21}^{5M}S_{12}^{5M}} & {S_{21}^{5M}S_{22}^{5M}} & {S_{12}^{5M}S_{22}^{5M}} & 1 \\S_{11}^{6M} & S_{21}^{6M} & S_{12}^{6M} & S_{22}^{6M} & \left( S_{11}^{6M} \right)^{2} & \left( S_{21}^{6M} \right)^{2} & \left( S_{12}^{6M} \right)^{2} & \left( S_{22}^{6M} \right)^{2} & {S_{11}^{6M}S_{21}^{6M}} & {S_{11}^{6M}S_{12}^{6M}} & {S_{11}^{6M}S_{22}^{6M}} & {S_{21}^{6M}S_{12}^{6M}} & {S_{21}^{6M}S_{22}^{6M}} & {S_{12}^{6M}S_{22}^{6M}} & 1 \\S_{11}^{7M} & S_{21}^{7M} & S_{12}^{7M} & S_{22}^{7M} & \left( S_{11}^{7M} \right)^{2} & \left( S_{21}^{7M} \right)^{2} & \left( S_{12}^{7M} \right)^{2} & \left( S_{22}^{7M} \right)^{2} & {S_{11}^{7M}S_{21}^{7M}} & {S_{11}^{7M}S_{12}^{7M}} & {S_{11}^{7M}S_{22}^{7M}} & {S_{21}^{7M}S_{12}^{7M}} & {S_{21}^{7M}S_{22}^{7M}} & {S_{12}^{7M}S_{22}^{7M}} & 1 \\S_{11}^{8M} & S_{21}^{8M} & S_{12}^{8M} & S_{22}^{8M} & \left( S_{11}^{8M} \right)^{2} & \left( S_{21}^{8M} \right)^{2} & \left( S_{12}^{8M} \right)^{2} & \left( S_{22}^{8M} \right)^{2} & {S_{11}^{8M}S_{21}^{8M}} & {S_{11}^{8M}S_{12}^{8M}} & {S_{11}^{8M}S_{22}^{8M}} & {S_{21}^{8M}S_{12}^{8M}} & {S_{21}^{8M}S_{22}^{8M}} & {S_{12}^{8M}S_{22}^{8M}} & 1 \\S_{11}^{9M} & S_{21}^{9M} & S_{12}^{9M} & S_{22}^{9M} & \left( S_{11}^{9M} \right)^{2} & \left( S_{21}^{9M} \right)^{2} & \left( S_{12}^{9M} \right)^{2} & \left( S_{22}^{9M} \right)^{2} & {S_{11}^{9M}S_{21}^{9M}} & {S_{11}^{9M}S_{12}^{9M}} & {S_{11}^{9M}S_{22}^{9M}} & {S_{21}^{9M}S_{12}^{9M}} & {S_{21}^{9M}S_{22}^{9M}} & {S_{12}^{9M}S_{22}^{9M}} & 1 \\S_{11}^{10M} & S_{21}^{10M} & S_{12}^{10M} & S_{22}^{10M} & \left( S_{11}^{10M} \right)^{2} & \left( S_{21}^{10M} \right)^{2} & \left( S_{12}^{10M} \right)^{2} & \left( S_{22}^{10M} \right)^{2} & {S_{11}^{10M}S_{21}^{10M}} & {S_{11}^{10M}S_{12}^{10M}} & {S_{11}^{10M}S_{22}^{10M}} & {S_{21}^{10M}S_{12}^{10M}} & {S_{21}^{10M}S_{22}^{10M}} & {S_{12}^{10M}S_{22}^{10M}} & 1 \\S_{11}^{11M} & S_{21}^{11M} & S_{12}^{11M} & S_{22}^{11M} & \left( S_{11}^{11M} \right)^{2} & \left( S_{21}^{11M} \right)^{2} & \left( S_{12}^{11M} \right)^{2} & \left( S_{22}^{11M} \right)^{2} & {S_{11}^{11M}S_{21}^{11M}} & {S_{11}^{11M}S_{12}^{11M}} & {S_{11}^{11M}S_{22}^{11M}} & {S_{21}^{11M}S_{12}^{11M}} & {S_{21}^{11M}S_{22}^{11M}} & {S_{12}^{11M}S_{22}^{11M}} & 1 \\S_{11}^{12M} & S_{21}^{12M} & S_{12}^{12M} & S_{22}^{12M} & \left( S_{11}^{12M} \right)^{2} & \left( S_{21}^{12M} \right)^{2} & \left( S_{12}^{12M} \right)^{2} & \left( S_{22}^{12M} \right)^{2} & {S_{11}^{12M}S_{21}^{12M}} & {S_{11}^{12M}S_{12}^{12M}} & {S_{11}^{12M}S_{22}^{12M}} & {S_{21}^{12M}S_{12}^{12M}} & {S_{21}^{12M}S_{22}^{12M}} & {S_{12}^{12M}S_{22}^{12M}} & 1 \\S_{11}^{13M} & S_{21}^{13M} & S_{12}^{13M} & S_{22}^{13M} & \left( S_{11}^{13M} \right)^{2} & \left( S_{21}^{13M} \right)^{2} & \left( S_{12}^{13M} \right)^{2} & \left( S_{22}^{13M} \right)^{2} & {S_{11}^{13M}S_{21}^{13M}} & {S_{11}^{13M}S_{12}^{13M}} & {S_{11}^{13M}S_{22}^{13M}} & {S_{21}^{13M}S_{12}^{13M}} & {S_{21}^{13M}S_{22}^{13M}} & {S_{12}^{13M}S_{22}^{13M}} & 1 \\S_{11}^{14M} & S_{21}^{14M} & S_{12}^{14M} & S_{22}^{14M} & \left( S_{11}^{14M} \right)^{2} & \left( S_{21}^{14M} \right)^{2} & \left( S_{12}^{14M} \right)^{2} & \left( S_{22}^{14M} \right)^{2} & {S_{11}^{14M}S_{21}^{14M}} & {S_{11}^{14M}S_{12}^{14M}} & {S_{11}^{14M}S_{22}^{14M}} & {S_{21}^{14M}S_{12}^{14M}} & {S_{21}^{14M}S_{22}^{14M}} & {S_{12}^{14M}S_{22}^{14M}} & 1 \\S_{11}^{15M} & S_{21}^{15M} & S_{12}^{15M} & S_{22}^{15M} & \left( S_{11}^{15M} \right)^{2} & \left( S_{21}^{15M} \right)^{2} & \left( S_{12}^{15M} \right)^{2} & \left( S_{22}^{15M} \right)^{2} & {S_{11}^{15M}S_{21}^{15M}} & {S_{11}^{15M}S_{12}^{15M}} & {S_{11}^{15M}S_{22}^{15M}} & {S_{21}^{15M}S_{12}^{15M}} & {S_{21}^{15M}S_{22}^{15M}} & {S_{12}^{15M}S_{22}^{15M}} & 1\end{pmatrix}\begin{pmatrix}d_{1} \\d_{2} \\d_{3} \\d_{4} \\d_{5} \\d_{6} \\d_{7} \\d_{8} \\d_{9} \\d_{10} \\d_{11} \\d_{12} \\d_{13} \\d_{14} \\d_{0}\end{pmatrix}}}\end{matrix}$

S₁₁ ^(p*), S₂₁ ^(p*), S₁₂ ^(p*), and S₂₂ ^(p*): the S parameter of thecorrection-data acquisition samples measured by the reference measuringsystem

S₁₁ ^(pM), S₂₁ ^(pM), S₁₂ ^(pM), and S₂₂ ^(pM): the S parameter of thecorrection-data acquisition samples measured by the actual measuringsystem $\begin{matrix}{\left\lbrack {{Numerical}\quad {Formula}\quad 7} \right\rbrack \quad} & \quad \\{S_{11}^{*} = {\begin{pmatrix}a_{1} & a_{2} & a_{3} & a_{4} & a_{5} & a_{6} & a_{7} & a_{8} & a_{9} & a_{10} & a_{11} & a_{12} & a_{13} & a_{14} & a_{0}\end{pmatrix}\begin{pmatrix}S_{11}^{M} \\S_{21}^{M} \\S_{12}^{M} \\S_{22}^{M} \\\left( S_{11}^{M} \right)^{2} \\\left( S_{21}^{M} \right)^{2} \\\left( S_{12}^{M} \right)^{2} \\\left( S_{22}^{M} \right)^{2} \\{S_{11}^{M}S_{21}^{M}} \\{S_{11}^{M}S_{12}^{M}} \\{S_{11}^{M}S_{22}^{M}} \\{S_{21}^{M}S_{12}^{M}} \\{S_{21}^{M}S_{22}^{M}} \\{S_{12}^{M}S_{22}^{M}} \\1\end{pmatrix}}} & {C2a} \\{\left\lbrack {{Numerical}\quad {Formula}\quad 8} \right\rbrack \quad} & \quad \\{S_{21}^{*} = {\begin{pmatrix}b_{1} & b_{2} & b_{3} & b_{4} & b_{5} & b_{6} & b_{7} & b_{8} & b_{9} & b_{10} & b_{11} & b_{12} & b_{13} & b_{14} & b_{0}\end{pmatrix}\begin{pmatrix}S_{11}^{M} \\S_{21}^{M} \\S_{12}^{M} \\S_{22}^{M} \\\left( S_{11}^{M} \right)^{2} \\\left( S_{21}^{M} \right)^{2} \\\left( S_{12}^{M} \right)^{2} \\\left( S_{22}^{M} \right)^{2} \\{S_{11}^{M}S_{21}^{M}} \\{S_{11}^{M}S_{12}^{M}} \\{S_{11}^{M}S_{22}^{M}} \\{S_{21}^{M}S_{12}^{M}} \\{S_{21}^{M}S_{22}^{M}} \\{S_{12}^{M}S_{22}^{M}} \\1\end{pmatrix}}} & {C2b} \\{\left\lbrack {{Numerical}\quad {Formula}\quad 9} \right\rbrack \quad} & \quad \\{S_{12}^{*} = {\begin{pmatrix}c_{1} & c_{2} & c_{3} & c_{4} & c_{5} & c_{6} & c_{7} & c_{8} & c_{9} & c_{10} & c_{11} & c_{12} & c_{13} & c_{14} & c_{0}\end{pmatrix}\begin{pmatrix}S_{11}^{M} \\S_{21}^{M} \\S_{12}^{M} \\S_{22}^{M} \\\left( S_{11}^{M} \right)^{2} \\\left( S_{21}^{M} \right)^{2} \\\left( S_{12}^{M} \right)^{2} \\\left( S_{22}^{M} \right)^{2} \\{S_{11}^{M}S_{21}^{M}} \\{S_{11}^{M}S_{12}^{M}} \\{S_{11}^{M}S_{22}^{M}} \\{S_{21}^{M}S_{12}^{M}} \\{S_{21}^{M}S_{22}^{M}} \\{S_{12}^{M}S_{22}^{M}} \\1\end{pmatrix}}} & {C2c} \\{\left\lbrack {{Numerical}\quad {Formula}\quad 10} \right\rbrack \quad} & \quad \\{S_{22}^{*} = {\begin{pmatrix}d_{1} & d_{2} & d_{3} & d_{4} & d_{5} & d_{6} & d_{7} & d_{8} & d_{9} & d_{10} & d_{11} & d_{12} & d_{13} & d_{14} & d_{0}\end{pmatrix}\begin{pmatrix}S_{11}^{M} \\S_{21}^{M} \\S_{12}^{M} \\S_{22}^{M} \\\left( S_{11}^{M} \right)^{2} \\\left( S_{21}^{M} \right)^{2} \\\left( S_{12}^{M} \right)^{2} \\\left( S_{22}^{M} \right)^{2} \\{S_{11}^{M}S_{21}^{M}} \\{S_{11}^{M}S_{12}^{M}} \\{S_{11}^{M}S_{22}^{M}} \\{S_{21}^{M}S_{12}^{M}} \\{S_{21}^{M}S_{22}^{M}} \\{S_{12}^{M}S_{22}^{M}} \\1\end{pmatrix}}} & {C2d}\end{matrix}$

S₁₁*, S₂₁*, S₁₂*, and S₂₂*: the S parameter of the target electroniccomponent assumed to be obtained by the reference measuring system

S₁₁ ^(M), S₂₁ ^(M), S₁₂ ^(M), and S₂₂ ^(M): the S parameter of thetarget electronic component measured by the actual measuring system

The measurement error correction method according to the presentinvention may be perfectly applied to the quality checking method ofelectronic components. In this case, in the quality checking method ofto electronic components, a target electronic component with requiredelectrical characteristics to be measured by a reference measuringsystem is measured by an actual measuring system with a measured resultnot agreeing with that measured by the reference measuring system so asto check quality based on the measured result.

In the checking method according to the present invention, theelectrical characteristics of the target electronic component measuredby the actual measuring system are corrected using the measurement errorcorrection method according to the present invention, and then, thetarget electronic component may be checked by comparing the correctedelectrical characteristics with the required electrical characteristics.Thereby, quality of the target electronic component can be checked withhigh accuracy.

According to the present invention, the following electronic componentcharacteristic measuring system may be proposed as a measuring systemcapable of performing the measurement error correction method describedabove.

A measuring system of electronic component characteristics comprisesmeasuring means for measuring electrical characteristics of a targetelectronic component, measured results of the measuring means do notagree with a reference measuring system; storing means for storingelectrical characteristics, which are measured by the referencemeasuring system, of a correction-data acquisition sample generating thesame electrical characteristics as arbitrary electrical characteristicsof the target electronic component; interrelating formula computingmeans for computing an interrelating formula between the electricalcharacteristics of the correction-data acquisition sample, which aremeasured by the measuring means, and the electrical characteristics ofthe correction-data acquisition sample, which are measured by thereference measuring system and stored in the storing means; andcorrecting means for correcting the electrical characteristics of thetarget electronic component to electrical characteristics assumed to beobtained by the reference measuring system by substituting theelectrical characteristics of the target electronic component measuredby the measuring means in the interrelating formula for computation.

When the measuring system according to the present invention isconfigured based on the analytical relative correction method, theinterrelating formula computing means may preferably comprise assumingmeans for assuming signal transfer patterns of both the measuringsystems during measurement to include measurement error factors;creating means for creating a theoretical equation for obtaining ameasurement true value of the actual measuring system in the signaltransfer pattern and creating a theoretical equation for obtaining ameasurement true value of the reference measuring system in the signaltransfer pattern; creating means for creating the interrelating formulacomprising an arithmetic expression, which includes an undeterminedcoefficient and directly and exclusively shows the relationship betweenthe measurement true value of the actual measuring system and themeasurement true value of the reference measuring system, based on boththe theoretical equations; measuring means for measuring electricalcharacteristics of the correction-data acquisition sample by thereference measuring system and the actual measuring system,respectively; and identifying means for identifying the undeterminedcoefficient by substituting the electrical characteristics of thecorrection-data acquisition sample measured by both the measuringsystems in the interrelating formula.

When the measuring system according to the present invention isconfigured based on the approximate relative correction method, theinterrelating formula computing means may preferably comprise creatingmeans for creating the interrelating formula comprising an expression ofdegree n (n is a natural number), which includes an undeterminedcoefficient and approximately shows the relationship between the valuemeasured by the actual measuring system and the value measured by thereference measuring system; measuring means for measuring electricalcharacteristics of the correction-data acquisition sample by thereference measuring system and the actual measuring system,respectively; and identifying means for identifying the undeterminedcoefficient by substituting the electrical characteristics of thecorrection-data acquisition sample measured by both the measuringsystems in the interrelating formula.

According to the present invention, in correcting results measured bythe actual measuring system to results measured by the referencemeasuring system, the correction is performed not by a conventionalabsolute correction method but by the relative correction method. Therelative correction method is a method as follows.

The relative correction method is a method for correcting the electriccharacteristics (sample true value+measurement errors of the actualmeasuring system) of a target electronic component measured by theactual measuring system (including actual measurement fixture) to theelectric characteristics (sample true value+measurement errors of thereference measuring system) assumed to be obtained by the referencemeasuring system (including reference measurement fixture). The relativecorrection method has a feature that the sample true value of a targetelectronic component is not limited to be known but may be unknown.

The present invention proposes the analytical relative correction methodand the approximate relative correction method as a relative correctionmethod. During correction by the analytical relative correction method,a signal transfer pattern including measurement error factors of boththe measuring systems should be assumed. In this case, the signaltransfer pattern may enough correspond to the measurement error factor,so that it is assumed to be arbitrary one. For such a signal transferpattern, conventional ones used in the absolute correction method may beemployed. The analytical relative correction method can correct theentire linear errors with high accuracy in principle. However, theanalytical relative correction method cannot correct nonlinear errors.Such features of the analytical relative correction method are the sameas those of the absolute correction method.

The approximate relative correction method is a correction method usingan approximate equation instead of the analytical equation when theanalytical equation becomes too complicated. In the approximate relativecorrection method, additional errors cannot be avoided becauseapproximate accuracy of the approximate equation absolutely has thelimit. However, the number of the correction-data acquisition samplescan be reduced in the approximate relative correction method. Also, itcan correct nonlinear errors.

As described above, according to the present invention, measuredresults, which do not agree with the reference measuring systemaccurately, can be corrected equally to the results measured by thereference measuring system.

Other features and advantages of the present invention will becomeapparent from the following description of the invention which refers tothe accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plan view showing an outlined arrangement of a measuringsystem for performing a measurement error correction method according tothe present invention;

FIG. 2 is a plan view showing an arrangement of a measurement fixturefor performing the measurement error correction method according to thepresent invention;

FIG. 3 is a block diagram showing a configuration of the measuringsystem for performing the measurement error correction method accordingto the present invention;

FIG. 4 is a back view showing an arrangement of a correction-dataacquisition sample and a target electronic component constituting themeasuring system for performing the measurement error correction methodaccording to the present invention;

FIG. 5 is a plan view showing an arrangement of the correction-dataacquisition sample constituting the measuring system for performing themeasurement error correction method according to the present invention;

FIG. 6 is an equivalent circuit diagram of the correction-dataacquisition sample constituting the measuring system for performing themeasurement error correction method according to the present invention;

FIG. 7 is a drawing of an example of a signal transfer pattern (errormodel) for use in performing a measurement error correction methodaccording to a first embodiment of the present invention;

FIG. 8 is a graph showing correction data obtained by performing themeasurement error correction method according to the first embodiment ofthe present invention;

FIG. 9 is a graph showing correction data obtained by performing themeasurement error correction method according to the first embodiment ofthe present invention;

FIG. 10 is a graph showing correction data obtained by performing themeasurement error correction method according to the first embodiment ofthe present invention;

FIG. 11 is a drawing of an example of a signal transfer pattern (errormodel) for use in performing a measurement error correction methodaccording to a second embodiment of the present invention;

FIG. 12 is a graph showing correction data obtained by performing themeasurement error correction method according to the first embodiment ofthe present invention;

FIG. 13 is a table showing correction data obtained by performing themeasurement error correction method according to the second embodimentof the present invention;

FIG. 14 is a table showing correction data obtained by performing ameasurement error correction method according to a third embodiment ofthe present invention;

FIG. 15 is a graph showing correction data obtained by performing themeasurement error correction method according to the second embodimentof the present invention and actual measured results; and

FIG. 16 is a graph showing correction data obtained by performing themeasurement error correction method according to the third embodiment ofthe present invention and actual measured results.

Although the present invention has been described in relation toparticular embodiments thereof, many other variations and modificationsand other uses will become apparent to those skilled in the art. It ispreferred, therefore, that the present invention be limited not by thespecific disclosure herein, but only by the appended claims.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

First Embodiment

According to a first embodiment, the present invention is incorporatedin a correction method of measurement errors when electricalcharacteristics of a surface-mount SAW (surface acoustic wave) filter,which is an electronic component targeted for measurement, are measuredby a measuring system having a network analyzer.

FIG. 1 is a plan view of an arrangement of a measuring system accordingto the embodiment; FIG. 2 is a plan view of an arrangement of ameasurement fixture; FIG. 3 is a block diagram of a configuration of anetwork analyzer of an actual measuring system; FIG. 4 is a back viewshowing an electronic component targeted for measurement and acorrection-data acquisition sample; FIG. 5 is a plan view of thecorrection-data acquisition sample; and FIG. 6 is an equivalent circuitdiagram of the correction-data acquisition sample.

A measuring system constituting a reference measuring system 1 and anactual measuring system 2, as shown in FIG. 1, comprises networkanalyzers 3A and 3B, coaxial cables 4A and 4B, and measurement fixtures5A and 5B. In addition, the network analyzer 3A and the measurementfixture 5A are provided in the reference measuring system 1 while thenetwork analyzer 3B and the measurement fixture 5B are provided in theactual measuring system 2.

The network analyzers 3A and 3B are measuring systems for measuringelectrical characteristics of electronic components used at a highfrequency and each has an input-output interface with two-port (port 1′and port 2′). To the ports 1′ and 2′, the coaxial cables 4A and 4B areconnected, respectively. The other ends of the coaxial cables 4A and 4Bare provided with coaxial cable connectors 6.

The measurement fixtures 5A and 5B, as shown in FIG. 2, comprise aninsulating substrate 7, a wiring connection 8, and coaxial connectors 9Aand 9B. The wiring connection 8 formed on a surface 7 a of theinsulating substrate 7 comprises signal transmission media 8 a and 8 band grounding lines 8 c to 8 f. On the surface 7 a of the insulatingsubstrate 7, the signal transmission media 8 a and 8 b extend from bothends of the substrate toward the center of the substrate, respectively,so that both extended ends are arranged in the center on the substratesurface 7 to oppose each other with a predetermined separating spacetherebetween. The grounding lines 8 c to 8 f are arranged in the centeron the substrate surface 7 on both sides of the signal transmissionmedia 8 a and 8 b, respectively. The lines 8 a and 8 b located on theside of the transmission medium 8 a and the lines 8 e and 8 f located onthe side of the transmission medium 8 b are arranged in the center onthe substrate surface 7 to oppose each other with a predeterminedseparating space (identical to that of the signal transmission media 8 aand 8 b) therebetween.

The signal transmission media 8 a and 8 b are connected to innerconductor contacts (not shown) of the coaxial connectors 9A and 9B atsubstrate ends. The grounding lines 8 c to 8 f are connected to a groundpattern (not shown) on the back surface of the substrate viathrough-hole connections 10. The grounding lines 8 c to 8 f are furtherconnected to outer conductor contacts (not shown) of the coaxialconnectors 9A and 9B via the ground pattern.

In FIG. 2, the measurement fixture 5A of the reference measuring system1 (referred to as a reference measurement fixture below) and themeasurement fixture 5B of the actual measuring system 2 (referred to asa actual measurement fixture below) have the same shape; however, theyare not necessarily identical. In particular, the actual measurementfixture 5B may have a shape different from the reference measurementfixture 5A, such as a shape suitable for an automatic sorting measuringsystem.

The network analyzer 3B constituting the actual measuring system 2, asshown in FIG. 3, comprises a network analyzer body 20 and a control unit21. The control unit 21 comprises a control unit body 22, a memory 23,an interrelation equation computing means 24, and a correcting means 25.

A target electronic component 11A and a correction-data acquisitionsample 11B, as shown in FIG. 4, comprise transmission medium terminals12 a and 12 b or pseudo-transmission medium terminals 14 a and 14 b, andgrounding terminals 12 c to 12 f or pseudo-grounding terminals 14 c to14 f, which are formed on back surfaces 11 a thereof. By abutting theback surfaces 11 a of the target electronic component 11A and thecorrection-data acquisition sample 11B on a surface 7 a of themeasurement fixture 5, the transmission medium terminals 12 a and 12 b(or the pseudo-transmission medium terminals 14 a and 14 b) and thegrounding terminals 12 c to 12 f (or pseudo-grounding terminals 14 c to14 f) are press-bonded on the signal transmission media 8 a and 8 b andthe grounding lines 8 c to 8 f, respectively. Thereby, the targetelectronic component 11A and the correction-data acquisition sample 11Bare mounted on the measurement fixtures 5A and 5B for measurement,respectively.

According to this embodiment, as the correction-data acquisition sample11B, a sample is prepared generating the same electrical characteristicsas arbitrary electrical characteristics of the target electroniccomponent 11A by measurement operation of the measuring systems 1 and 2.Moreover, according to this embodiment, as the correction-dataacquisition sample 11B also prepared are a plurality (six, for example)of samples 11B_(1 to 6) having the electrical characteristics differentfrom each other generated by the measuring system.

The correction-data acquisition samples 11B_(1 to 6), as shown in FIG.5, comprise a frame 13 having the same shape as that of the targetelectronic component 11A. The frame 13 is provided with thepseudo-transmission medium terminals 14 a and 14 b and thepseudo-grounding terminals 14 c to 14 f, which respectively have thesame arrangements as those of the transmission medium terminals 12 a and12 b and the grounding terminals 12 c to 12 f of the target electroniccomponent 11A. These pseudo-transmission medium terminals 14 a and 14 band the pseudo-grounding terminals 14 c to 14 f extend from the bottomsurface of the frame 13 to the top surface 13 a via side surfaces. Theextended ends on the top surface 13 a of the pseudo-transmission mediumterminals 14 a and 14 b and the pseudo-grounding terminals 14 c to 14 fconstitute mounting terminals 15 a to 15 f, respectively.

Between the mounting terminals neighboring with each other (15 a and 15b), (15 a and 15 d), (15 a and 15 c), (15 b and 15 e), and (15 b and 15f), electrical characteristic adjusting elements 16 a to 16 e made ofresistance elements are mounted.

In the correction-data acquisition samples 11B_(1 to 6) having theelectrical characteristic adjusting elements 16 a to 16 e mountedthereon in such a manner, as shown in the equivalent circuit of FIG. 6,between input and output terminals 17A and 17B, a resistance componentR1 is arranged. Between the input and output terminals 17A and 17B andthe ground potential, resistance components R2 and R3 are arranged.Arbitrarily setting electrical characteristics (resistance value for theresistance element) of the electrical characteristic adjusting elements16 a to 16 e enables the characteristics (electrical characteristicsmeasured by the measuring system) of the correction-data acquisitionsamples 11B_(1 to 6) to be randomly set. According to this embodiment,it is not necessary to set precise values of electrical characteristicsgenerated by the measurement operation of the measuring system to thecorrection-data acquisition samples 11B_(1 to 6) in advance. Therefore,the cost of producing the correction-data acquisition samples11B_(1 to 6) can be reduced.

A correction method (analytical relative correction method) ofmeasurement errors according to this embodiment and performed by themeasuring system will be described below.

First, the outline will be described. As a common problem in thehigh-frequency characteristic measurement of a noncoaxial-type sample,the measured result of the characteristics (a scattering coefficient,etc.) differs from one measuring system to another. Specifically, themeasured result of the correction-data acquisition sample 11B by themeasuring system (reference measuring system 1) including a fixture forquality assurance to users (reference measurement fixture 5A) differsfrom the measured result of the correction-data acquisition sample 11Bby the measuring system (actual measuring system 2) including a fixturefor use on delivery inspection (actual measurement fixture 5B). Such adiscrepancy between measured results disables quality assurance to userson delivery inspection.

Then, according to this embodiment, in order to overcome such a problem,the measured result by the reference measuring system 1 is assumed fromthe measured result by the actual measuring system by computation usinga relative correction method.

The principle of a correction method (analytical relative correctionmethod) according to this embodiment, which corresponds to a two-portunbalanced measuring system, will be described below.

First, error factors of the measuring systems (the reference measuringsystem 1 and the actual measuring system 2) are modeled according to asignal transfer pattern shown in FIG. 7. The signal transfer patternshown in FIG. 7 is identical with a 2-Port error model that is generallyused.

The signal transfer pattern (error model) shown in FIG. 7 is anextremely accurate model for a coaxial measurement system. Strictlyspeaking, it is not so accurate for a noncoaxial measurement system,which is caused by the fact that the treatment of leakage is partiallyalienated from actual physical phenomena.

According to this embodiment, this signal transfer pattern (error model)is adopted because the model has been in worldwide use for a long timewhile even knowing that, strictly speaking, it is not accurate for anoncoaxial measurement system. However, according to need, a moreaccurate signal transfer pattern may be produced so as to deduce aformula of a relative correction method therefrom. Although the signaltransfer pattern shown in FIG. 7 may lead to some error when ameasurement fixture develops leakage, the error is not very large whenthere is small leakage in the measurement fixture (having goodisolation).

If entire error factors are identified in the signal transfer pattern,from measured values (S_(11M), S_(21M), S_(12M), and S_(22M)) of thecorrection-data acquisition samples 11B_(1 to 6), scattering coefficienttrue values (S_(11A), S_(21A), S_(12A), and S_(22A)) are obtained bytheoretical equations (A1a) to (A1d). The theoretical equations (A1a) to(A1d) can be deduced by building the equations on the signal transferpattern shown in FIG. 7. $\begin{matrix}{\left\lbrack {{Numerical}\quad {Formula}\quad 11} \right\rbrack \quad} & \quad \\{S_{11A} = {\left( {{\left( {S_{11M} - E_{D\quad F}} \right)*{\left( {{E_{S\quad R}*{\left( {S_{22M} - E_{D\quad R}} \right)/E_{R\quad R}}} + 1} \right)/E_{R\quad F}}} - {E_{L\quad F}*\left( {S_{12M} - E_{X\quad R}} \right)*{\left( {S_{21M} - E_{X\quad F}} \right)/\left( {E_{T\quad F}*E_{T\quad R}} \right)}}} \right)/\left( {{\left( {{E_{S\quad F}*{\left( {S_{11M} - E_{D\quad F}} \right)/E_{R\quad F}}} + 1} \right)*\left( {{E_{S\quad R}*{\left( {S_{22M} - E_{D\quad R}} \right)/E_{R\quad R}}} + 1} \right)} - {E_{L\quad F}*E_{L\quad R}*\left( {S_{12M} - E_{X\quad R}} \right)*{\left( {S_{21M} - E_{X\quad F}} \right)/\left( {E_{T\quad F}*E_{T\quad R}} \right)}}} \right)}} & ({A1a}) \\{S_{21A} = {\left( {S_{21M} - E_{X\quad F}} \right)*{\left( {{\left( {E_{S\quad R} - E_{L\quad F}} \right)*{\left( {S_{22M} - E_{D\quad R}} \right)/E_{R\quad R}}} + 1} \right)/\left( {E_{T\quad F}*\left( {{\left( {{E_{S\quad F}*{\left( {S_{11M} - E_{D\quad F}} \right)/E_{R\quad F}}} + 1} \right)*\left( {{E_{S\quad R}*{\left( {S_{22M} - E_{D\quad R}} \right)/E_{R\quad R}}} + 1} \right)} - {E_{L\quad F}*E_{L\quad R}*\left( {S_{12M} - E_{X\quad R}} \right)*{\left( {S_{21M} - E_{X\quad F}} \right)/\left( {E_{T\quad F}*E_{T\quad R}} \right)}}} \right)} \right)}}} & ({A1b}) \\{S_{12A} = {\left( {{\left( {E_{S\quad F} - E_{L\quad R}} \right)*{\left( {S_{11M} - E_{D\quad F}} \right)/E_{R\quad F}}} + 1} \right)*{\left( {S_{12M} - E_{X\quad R}} \right)/\left( {E_{T\quad R}*\left( {{\left( {{E_{S\quad F}*{\left( {S_{{11M}\quad} - E_{D\quad F}} \right)/E_{R\quad F}}} + 1} \right)*\left( {{E_{S\quad R}*{\left( {S_{22M} - E_{D\quad R}} \right)/E_{R\quad R}}} + 1} \right)} - {E_{L\quad F}*E_{L\quad R}*\left( {S_{12M} - E_{X\quad R}} \right)*{\left( {S_{21M} - E_{X\quad F}} \right)/\left( {E_{T\quad F}*E_{T\quad R}} \right)}}} \right)} \right)}}} & ({A1c}) \\{S_{22A} = {\left( {{\left( {{E_{S\quad F}*{\left( {S_{11M} - E_{D\quad F}} \right)/E_{R\quad F}}} + 1} \right)*{\left( {S_{22M} - E_{D\quad R}} \right)/E_{R\quad R}}} - {E_{L\quad R}*\left( {S_{12M} - E_{X\quad R}} \right)*{\left( {S_{21M} - E_{X\quad F}} \right)/\left( {E_{T\quad F}*E_{T\quad R}} \right)}}} \right)/\left( {{\left( {{E_{S\quad F}*{\left( {S_{11M} - E_{D\quad F}} \right)/E_{R\quad F}}} + 1} \right)*\left( {{E_{S\quad R}*{\left( {S_{22M} - E_{D\quad R}} \right)/E_{R\quad R}}} + 1} \right)} - {E_{L\quad F}*E_{L\quad R}*\left( {S_{12M} - E_{X\quad R}} \right)*{\left( {S_{21M} - E_{X\quad F}} \right)/\left( {E_{T\quad F}*E_{T\quad R}} \right)}}} \right)}} & ({A1d})\end{matrix}$

After the correction-data acquisition samples 11B_(1 to 6), in which thescattering coefficient true values are values (S_(11A), S_(21A),S_(12A), and S_(22A)), are measured, in the reference measuring system1, the scattering coefficient values (S_(11D), S_(21D), S_(12D), andS_(22D)) are measured while in the actual reference measuring system 2,the scattering coefficient values (S_(11M), S_(21M), S_(12M), andS_(22M)) are measured.

In descriptions below, the error factor of the reference measuringsystem 1 (the measurement fixture 5A) will be expressed by adding asubscript 1 to the name of the error factor, as E_(DP1), for example,while the error factor of the actual measuring system 2 (the measurementfixture 5B) will be expressed by adding a subscript 2 to the name of theerror factor, as E_(XR2). The name of the error factor corresponds tothat shown in FIG. 7.

Wherein, the scattering-coefficient true values (S_(11A), S_(21A),S_(12A), and S_(22A)) of the correction-data acquisition samples 11B,and the error-factor values of the reference measuring system 1 (themeasurement fixture 5A) and the actual measuring system 2 (themeasurement fixture 5B) are practically impossible to be known. Whereas,the measured values (S_(11D), S_(21D), S_(12D), and S_(22D)) by thereference measuring system 1 and the measured values (S_(11M), S_(21M),S_(12M), and S_(22M)) by the actual measuring system 2 are possible tobe known by actual measurement.

It is an object of the relative correction method according to thisembodiment to obtain the measured values by the reference measuringsystem 1 from the measured values by the actual measuring system 2.

It is assumed that the error-factors of the reference measuring system 1(the measurement fixture 5A) and the actual measuring system 2 (themeasurement fixture 5B) are identified. At this time, when theoreticalarithmetic equations showing the relationship between each of themeasured values by the reference measuring system 1 and the actualmeasuring system 2 and its scattering coefficient are considered on thebasis of the aforementioned theoretical equations (A1a) to (A1d), thefollowing theoretical arithmetic equations (A2a) to (A2d) andtheoretical arithmetic equations (A3a) to (A3d) are effected. Thesetheoretical arithmetic equations show that the sample scatteringcoefficients can be calculated from the measured values by the measuringsystems 1 and 2 (the measurement fixtures 5A and 5B) as long as theerror factors in the measuring systems 1 and 2 (the measurement fixtures5A and 5B) are identified. $\begin{matrix}{\left\lbrack {{Numerical}\quad {Formula}\quad 12} \right\rbrack \quad} & \quad \\{S_{11A} = {\left( {{\left( {S_{11D} - E_{D\quad {F1}}} \right)*{\left( {{E_{S\quad {R1}}*{\left( {S_{22D} - E_{D\quad {R1}}} \right)/E_{R\quad {R1}}}} + 1} \right)/E_{R\quad {F1}}}} - {E_{L\quad {F1}}*\left( {S_{12D} - E_{X\quad {R1}}} \right)*{\left( {S_{21D} - E_{X\quad {F1}}} \right)/\left( {E_{T\quad {F1}}*E_{T\quad {R1}}} \right)}}} \right)/\left( {{\left( {{E_{S\quad {F1}}*{\left( {S_{11D} - E_{D\quad {F1}}} \right)/E_{R\quad {F1}}}} + 1} \right)*\left( {{E_{S\quad {R1}}*{\left( {S_{22D} - E_{D\quad {R1}}} \right)/E_{R\quad {R1}}}} + 1} \right)} - {E_{L\quad {F1}}*E_{L\quad {R1}}*\left( {S_{12D} - E_{X\quad {R1}}} \right)*{\left( {S_{21D} - E_{X\quad {F1}}} \right)/\left( {E_{T\quad {F1}}*E_{T\quad {R1}}} \right)}}} \right)}} & ({A2a}) \\{S_{21A} = {\left( {S_{21D} - E_{X\quad {F1}}} \right)*{\left( {{\left( {E_{S\quad {R1}} - E_{L\quad {F1}}} \right)*{\left( {S_{22D} - E_{D\quad {R1}}} \right)/E_{R\quad {R1}}}} + 1} \right)/\left( {E_{T\quad {F1}}*\left( {{\left( {{E_{S\quad {F1}}*{\left( {S_{11D} - E_{D\quad {F1}}} \right)/E_{R\quad {F1}}}} + 1} \right)*\left( {{E_{S\quad {R1}}*{\left( {S_{22D} - E_{D\quad {R1}}} \right)/E_{R\quad {R1}}}} + 1} \right)} - {E_{L\quad {F1}}*E_{L\quad {R1}}*\left( {S_{12D} - E_{X\quad {R1}}} \right)*{\left( {S_{21D} - E_{X\quad {F1}}} \right)/\left( {E_{T\quad {F1}}*E_{T\quad {R1}}} \right)}}} \right)} \right)}}} & ({A2b}) \\{S_{12A} = {\left( {{\left( {E_{S\quad {F1}} - E_{L\quad {R1}}} \right)*{\left( {S_{11D} - E_{D\quad {F1}}} \right)/E_{R\quad {F1}}}} + 1} \right)*{\left( {S_{12D} - E_{X\quad {R1}}} \right)/\left( {E_{T\quad {R1}}*\left( {{\left( {{E_{S\quad {F1}}*{\left( {S_{{11D}\quad} - E_{D\quad {F1}}} \right)/E_{R\quad {F1}}}} + 1} \right)*\left( {{E_{S\quad {R1}}*{\left( {S_{22D} - E_{D\quad {R1}}} \right)/E_{R\quad {R1}}}} + 1} \right)} - {E_{L\quad {F1}}*E_{L\quad {R1}}*\left( {S_{12D} - E_{X\quad {R1}}} \right)*{\left( {S_{21D} - E_{X\quad {F1}}} \right)/\left( {E_{T\quad {F1}}*E_{T\quad {R1}}} \right)}}} \right)} \right)}}} & ({A2c}) \\{S_{22A} = {\left( {{\left( {{E_{S\quad {F1}}*{\left( {S_{11D} - E_{D\quad {F1}}} \right)/E_{R\quad {F1}}}} + 1} \right)*{\left( {S_{22D} - E_{D\quad {R1}}} \right)/E_{R\quad {R1}}}} - {E_{L\quad {R1}}*\left( {S_{12D} - E_{X\quad {R1}}} \right)*{\left( {S_{21D} - E_{X\quad {F1}}} \right)/\left( {E_{T\quad {F1}}*E_{T\quad {R1}}} \right)}}} \right)/\left( {{\left( {{E_{S\quad {F1}}*{\left( {S_{11D} - E_{D\quad {F1}}} \right)/E_{R\quad {F1}}}} + 1} \right)*\left( {{E_{S\quad {R1}}*{\left( {S_{22D} - E_{D\quad {R1}}} \right)/E_{R\quad {R1}}}} + 1} \right)} - {E_{L\quad {F1}}*E_{L\quad {R1}}*\left( {S_{12D} - E_{X\quad {R1}}} \right)*{\left( {S_{21D} - E_{X\quad {F1}}} \right)/\left( {E_{T\quad {F1}}*E_{T\quad {R1}}} \right)}}} \right)}} & ({A2d}) \\{\left\lbrack {{Numerical}\quad {Formula}\quad 13} \right\rbrack \quad} & \quad \\{S_{11A} = {\left( {{\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {{E_{S\quad {R2}}*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} + 1} \right)/E_{R\quad {F2}}}} - {E_{L\quad {F2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}}} \right)/\left( {{\left( {{E_{S\quad {F2}}*{\left( {S_{11M} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} + 1} \right)*\left( {{E_{S\quad {R2}}*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} + 1} \right)} - {E_{L\quad {F2}}*E_{L\quad {R2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}}} \right)}} & ({A3a}) \\{S_{21A} = {\left( {S_{21M} - E_{X\quad {F2}}} \right)*{\left( {{\left( {E_{S\quad {R2}} - E_{L\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} + 1} \right)/\left( {E_{T\quad {F2}}*\left( {{\left( {{E_{S\quad {F2}}*{\left( {S_{11M} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} + 1} \right)*\left( {{E_{S\quad {R2}}*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} + 1} \right)} - {E_{L\quad {F2}}*E_{L\quad {R2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}}} \right)} \right)}}} & ({A3b}) \\{S_{12A} = {\left( {{\left( {E_{S\quad {F2}} - E_{L\quad {R2}}} \right)*{\left( {S_{11M} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} + 1} \right)*{\left( {S_{12M} - E_{X\quad {R2}}} \right)/\left( {E_{T\quad {R2}}*\left( {{\left( {{E_{S\quad {F2}}*{\left( {S_{{11M}\quad} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} + 1} \right)*\left( {{E_{S\quad {R2}}*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} + 1} \right)} - {E_{L\quad {F2}}*E_{L\quad {R2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}}} \right)} \right)}}} & ({A3c}) \\{S_{22A} = {\left( {{\left( {{E_{S\quad {F2}}*{\left( {S_{11M} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} + 1} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} - {E_{L\quad {R2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}}} \right)/\left( {{\left( {{E_{S\quad {F2}}*{\left( {S_{11M} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} + 1} \right)*\left( {{E_{S\quad {R2}}*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} + 1} \right)} - {E_{L\quad {F2}}*E_{L\quad {R2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}}} \right)}} & ({A3d})\end{matrix}$

By the way, if the same sample is measured by both the referencemeasuring system 1 and the actual measuring system 2, the samplescattering coefficient becomes identical between the theoreticalarithmetic equations (A2a) to (A2d) and theoretical arithmetic equations(A3a) to (A3d). Then, when the sample scattering coefficients (S_(11A),S_(21A), S_(12A), and S_(22A)) are eliminated from each of thetheoretical arithmetic equations (A2a) to (A2d) and theoreticalarithmetic equations (A3a) to (A3d), the following interrelationequations (A4a) to (A4d) are obtained. The interrelation equations (A4a)to (A4d) show the relationship between the measured results by thereference measuring system 1 and by the actual measuring system 2.$\begin{matrix}{\left\lbrack {{Numerical}\quad {Formula}\quad 14} \right\rbrack \quad} & \quad \\{S_{11D} = {E_{D\quad {F1}} + {E_{R\quad {F1}}*{\left( \left( {{{- E_{S\quad {R1}}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} + {E_{L\quad {F2}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} - {E_{L\quad {F2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}} + {E_{L\quad {F1}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}} - {\left( {S_{11M} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} \right) \right)/\left( {{E_{S\quad {F2}}*E_{S\quad {R1}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} - {E_{S\quad {F1}}*E_{S\quad {R1}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} - {E_{L\quad {F2}}*E_{S\quad {F2}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} + {E_{L\quad {F2}}*E_{S\quad {F1}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} - {E_{S\quad {R1}}*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} + {E_{L\quad {F2}}*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} + {E_{L\quad {F2}}*E_{S\quad {F2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}} - {E_{L\quad {F1}}*E_{S\quad {F2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}} - {E_{L\quad {F2}}*E_{L\quad {R1}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}} + {E_{L\quad {F1}}*E_{L\quad {R1}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}} + {E_{S\quad {F2}}*{\left( {S_{11M} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} - {E_{S\quad {F1}}*{\left( {S_{11M} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} - 1} \right)}}}} & ({A4a}) \\{\left\lbrack {{Numerical}\quad {Formula}\quad 15} \right\rbrack \quad} & \quad \\{S_{21D} = {E_{X\quad {F1}} + {E_{T\quad {F1}}*{\left( {{- \left( {S_{21M} - E_{X\quad {F2}}} \right)}*\left( {{E_{S\quad {R1}}*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} - {E_{L\quad {F1}}*\left( {S_{22M} - E_{D\quad {R2}}} \right)*{/E_{R\quad {R2}}}} + 1} \right)} \right)/\quad \left( {E_{T\quad {F2}}\quad*\left( {{E_{S\quad {F2}}*E_{S\quad {R1}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} - {E_{S\quad {F1}}*E_{S\quad {R1}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} - {E_{L\quad {F2}}*E_{S\quad {F2}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} + {E_{L\quad {F2}}*E_{S\quad {F1}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} - {E_{S\quad {R1}}*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} + {E_{L\quad {F2}}*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} + {E_{L\quad {F2}}*E_{S\quad {F2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}} - {E_{L\quad {F1}}*E_{S\quad {F2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}} - {E_{L\quad {F2}}*E_{L\quad {R1}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E\quad T_{\quad {R2}}} \right)}} + {E_{L\quad {F1}}*E_{L\quad {R1}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}} + {E_{S\quad {F2}}*{\left( {S_{11M} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} - {E_{S\quad {F1}}*{\left( {S_{11M} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} - 1} \right)} \right)}}}} & ({A4b}) \\{\left\lbrack {{Numerical}\quad {Formula}\quad 16} \right\rbrack \quad} & \quad \\{S_{12D} = {E_{X\quad {R1}} + {E_{TR1}*\left( {\left( {{{- E_{S\quad {F1}}}*{\left( {S_{11M} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} + {E_{L\quad {R1}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)}} \right)/\quad \left( {E_{T\quad {R2}}\quad*{\left( {{E_{S\quad {F1}}*E_{S\quad {R2}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} - {E_{L\quad {R2}}*E_{S\quad {R2}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} - {E_{S\quad {F1}}*E_{S\quad {R1}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} + {E_{L\quad {R2}}*E_{S\quad {R1}}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/\left( {E_{R\quad {F2}}*E_{R\quad {R2}}} \right)}} + {E_{S\quad {R2}}*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} - {E_{S\quad {R1}}*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {R2}}}} + {E_{L\quad {R2}}*E_{S\quad {R2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}} - {E_{L\quad {R1}}*E_{S\quad {R2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}} - {E_{L\quad {F1}}*E_{L\quad {R2}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}} + {E_{L\quad {F1}}*E_{L\quad {R1}}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*{\left( {S_{21M} - E_{X\quad {F2}}} \right)/\left( {E_{T\quad {F2}}*E_{T\quad {R2}}} \right)}} - {E_{S\quad {F1}}*{\left( {S_{11M} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} + {E_{L\quad {R2}}*{\left( {S_{11M} - E_{D\quad {F2}}} \right)/E_{R\quad {F2}}}} - 1} \right)\left\lbrack {{Numerical}\quad {Formula}{\quad \quad}17} \right\rbrack}} \right.} \right.}}} & ({A4c}) \\{\left. {S_{22D} = {E_{DR1} + {E_{RR1}*\left( {\left( {{- E_{SF1}}*\left( {S_{11M} - E_{DF2}} \right)*{\left( {S_{22M} - E_{D\quad {R2}}} \right)/E_{R\quad {F2}}}*E_{RR2}} \right) + {E_{LR2}*\left( {S_{11M} - E_{D\quad {F2}}} \right)*{\left( {S_{22M} - E_{DR2}} \right)/\left( {E_{RF2}*E_{RR2}} \right)}} - {\left( {S_{22M} - E_{DR2}} \right)/E_{RR2}} - {E_{LR2}*\left( {S_{12M} - E_{XR2}} \right)*{\left( {S_{21M} - E_{XF2}} \right)/\left( {E_{TF2}*E_{TF2}} \right)}} + {E_{LR1}*\left( {S_{12M} - E_{XR2}} \right)*{\left( {S_{21M} - E_{XF2}} \right)/\left( {E_{TF2}*E_{TF2}} \right)}}} \right)}}} \right)/\left( {{E_{SF1}*E_{SR2}*\left( {S_{11M} - E_{DF2}} \right)*{\left( {S_{22M} - E_{DR2}} \right)/\left( {E_{RF2}*E_{RR2}} \right)}} - {E_{LR2}*E_{SR2}*\left( {S_{11M} - E_{DF2}} \right)*{\left( {S_{22M} - E_{DR2}} \right)/\left( {E_{RF2}*E_{RR2}} \right)}} - {E_{SF1}*E_{SR1}*\left( {S_{11M} - E_{DF2}} \right)*{\left( {S_{22M} - E_{DR2}} \right)/\left( {E_{RF2}*E_{RR2}} \right)}} + {E_{LR2}*E_{SR1}*\left( {S_{11M} - E_{DF2}} \right)*{\left( {S_{22M} - E_{DR2}} \right)/\left( {E_{RF2}*E_{RR2}} \right)}} + {E_{SR2}*{\left( {S_{22M} - E_{DR2}} \right)/E_{RR2}}} - {E_{SR1}*{\left( {S_{22M} - E_{DR2}} \right)/E_{RR2}}} + {E_{LR2}*E_{SR2}*\left( {S_{12M} - E_{XR2}} \right)*{\left( {S_{21M} - E_{XF2}} \right)/\left( {E_{TF2}*E_{TR2}} \right)}} - {E_{LR1}*E_{SR2}*\left( {S_{12M} - E_{XR2}} \right)*{\left( {S_{21M} - E_{XF2}} \right)/\left( {E_{TF2}*E_{TR2}} \right)}} - {E_{LF1}*E_{LR2}*\left( {S_{12M} - E_{XR2}} \right)*{\left( {S_{21M} - E_{XF2}} \right)/\left( {E_{TF2}*E_{TR2}} \right)}} + {E_{LF1}*E_{LR1}*\left( {S_{12M} - E_{XR2}} \right)*{\left( {S_{21M} - E_{XF2}} \right)/\left( {E_{TF2}*E_{TR2}} \right)}} - {E_{SF1}*{\left( {S_{11M} - E_{DF2}} \right)/E_{RF2}}} + {E_{LR2}*{\left( {S_{11M} - E_{DF2}} \right)/E_{RF2}}} - 1} \right)} & ({A4d})\end{matrix}$

The interrelation equations (A4a) to (A4d) obtained in such a manner arerearranged with regard to the measured values (S_(11M), S₂₁M, S₁₂M, andS₂₂M) measured by the actual measuring system 2 (the measurement fixture5B). Furthermore, in order to simplify the rearranged equations, theerror factors are appropriately substituted for variables. Then, thefollowing interrelation equations (A5a) to (A5d) are obtained. In theinterrelation equations OLE_LINK1 (A5a) to (A5d) OLE_LINK1, a₀, a₁, a₃,b₀, b₁, b₃, c₀, c₁, c₃, d₀, d₁, e₀, e₁, e₃, f₀, f₁, k, and m, which are18 coefficients in total, and E_(XF1), E_(XR1), E_(XF2), and E_(XR2),which are four coefficients in total, are undetermined coefficientsincluding in the interrelation equations. The undetermined coefficientsused in denominators in right-side fractional sections of equations withregard to S_(11D), S_(21D), S_(22D), and S_(12D) use the same symbols,showing that each coefficient is entirely identical with each other.$\begin{matrix}{\left\lbrack {{Numerical}\quad {Formula}\quad 1\quad 8} \right\rbrack \quad} & \quad \\{S_{11D} = {\left( {{c_{0}*S_{11M}*S_{22M}} + {c_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*\left( {S_{21M} - E_{X\quad {F2}}} \right)} + {k*c_{0}*S_{11M}} + {c_{3}*S_{22M}} + {k*c_{3}}} \right)/\left( {{a_{0}*S_{11M}*S_{22M}} + {a_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*\left( {S_{21M} - E_{X\quad {F2}}} \right)} + {k*a_{0}*S_{11M}} + {a_{3}*S_{22M}} + {k*a_{3}}} \right)}} & ({A5a}) \\{S_{21D} = {E_{X\quad {F1}} + {\left( {{d_{0}*\left( {S_{21M} - E_{X\quad {F2}}} \right)*S_{22M}} + {d_{1}*\left( {S_{21M} - E_{X\quad {F2}}} \right)}} \right)/\left( {{a_{0}*S_{11M}*S_{22M}} + {a_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*\left( {S_{21M} - E_{X\quad {F2}}} \right)} + {k*a_{0}*S_{11M}} + {a_{3}*S_{22M}} + {k*a_{3}}} \right)}}} & ({A5b}) \\{S_{12D} = {E_{X\quad {R1}} + {\left( {{e_{0}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*S_{11M}} + {e_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)}} \right)/\left( {{b_{0}*S_{11M}*S_{22M}} + {b_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*\left( {S_{21M} - E_{X\quad {F2}}} \right)} + {m*b_{0}*S_{11M}} + {b_{3}*S_{22M}} + {m*b_{3}}} \right)}}} & ({A5c}) \\{S_{22D} = {\left( {{f_{0}*S_{11M}*S_{22M}} + {f_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*\left( {S_{21M} - E_{X\quad {F2}}} \right)} + {m*f_{0}*S_{22M}} + {f_{3}*S_{11M}} + {m*f_{3}}} \right)/\left( {{b_{0}*S_{11M}*S_{22M}} + {b_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*\left( {S_{21M} - E_{X\quad {F2}}} \right)} + {m*b_{0}*S_{22M}} + {b_{3}*S_{11M}} + {m*b_{3}}} \right)}} & ({A5d})\end{matrix}$

In the interrelation equations (A5a) to (A5d), which are produced insuch a manner, it is enough to determine the aforementioned 22undetermined coefficients. These interrelation equations (A5a) to (A5d)are rational expressions, and leakages, in which two variables (a₀ andb₀, for example) are set to be one as references, may be mostly assumednegligible.

From the above, the number of undetermined coefficients of theinterrelation equations (A5a) to (A5d) is to practically be 16.

Also, when one sample is measured, four equations are obtained.

From the above, when the four correction-data acquisition samples 11Bare measured, the undetermined coefficients including in theinterrelation equations (A5a) to (A5d) can be theoretically determined.

However, the undetermined coefficients k and m appear as products byother coefficients, and it is not easy to identify the undeterminedcoefficients appearing in the interrelation equations (A5a) to (A5d).Then, although the required number of the correction-data acquisitionsamples 11B increases in some degree, the calculation of theundetermined coefficients can be facilitated by treating the products ofthe coefficients k and m by other coefficients as independent variablesso as to linearize the equations. Results of these substitutions areshown in the following interrelation equations (A6a) to (A6d). In theseinterrelation equations, the undetermined coefficients are a₀ to a₄, b₀to b₄, c₀ to c₄, d₀, d₁, e₀ to e₄, f₀, f₁, which are 22 coefficients intotal, and E_(XF1), E_(XR1), E_(XF2), and E_(XR2), which are fourcoefficients in total. $\begin{matrix}{\left\lbrack {{Numerical}\quad {Formula}\quad 1\quad 9} \right\rbrack \quad} & \quad \\{S_{11D} = {\left( {{c_{0}*S_{11M}*S_{22M}} + {c_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*\left( {S_{21M} - E_{X\quad {F2}}} \right)} + {c_{2}*S_{11M}} + {c_{3}*S_{22M}} + c_{4}} \right)/\left( {{a_{0}*S_{11M}*S_{22M}} + {a_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*\left( {S_{21M} - E_{X\quad {F2}}} \right)} + {a_{2}*S_{11M}} + {a_{3}*S_{22M}} + a_{4}} \right)}} & ({A6a}) \\{S_{21D} = {E_{X\quad {F1}} + {\left( {{d_{0}*\left( {S_{21M} - E_{X\quad {F2}}} \right)*S_{22M}} + {d_{1}*S_{21M}}} \right)/\left( {{a_{0}*S_{11M}*S_{22M}} + {a_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*\left( {S_{21M} - E_{X\quad {F2}}} \right)} + {a_{2}*S_{11M}} + {a_{3}*S_{22M}} + a_{4}} \right)}}} & ({A6b}) \\{S_{12D} = {E_{X\quad {R1}} + {\left( {{e_{0}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*S_{11M}} + {e_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)}} \right)/\left( {{b_{0}*S_{11M}*S_{22M}} + {b_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*\left( {S_{21M} - E_{X\quad {F2}}} \right)} + {b_{2}*S_{11M}} + {b_{3}*S_{22M}} + b_{4}} \right)}}} & ({A6c}) \\{S_{22D} = {\left( {{f_{0}*S_{11M}*S_{22M}} + {f_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*\left( {S_{21M} - E_{X\quad {F2}}} \right)} + {f_{2}*S_{11M}} + {f_{3}*S_{22M}} + f_{4}} \right)/\left( {{b_{0}*S_{11M}*S_{22M}} + {b_{1}*\left( {S_{12M} - E_{X\quad {R2}}} \right)*\left( {S_{21M} - E_{X\quad {F2}}} \right)} + {b_{2}*S_{11M}} + {b_{3}*S_{22M}} + b_{4}} \right)}} & ({A6d})\end{matrix}$

In the interrelation equations (A6a) to (A6d), the four coefficientsE_(XF1), E_(XR1), E_(XF2), and E_(XR2) are so-called leaks betweenports, and they may be negligible in the measuring systems 1 and 2(measurement fixtures 5A and 5B) with excellent isolation. In this case,it is enough to simply set these undetermined coefficients to be zero.Even when being not negligible, these leaks between ports can be simplyestimated. For example, the measured value of the scattering coefficientby the measuring systems 1 and 2 (measurement fixtures 5A and 5B)without the correction-data acquisition sample 11B attached thereto maybe appropriated for the leak between ports. The substitution ofvariables performed by identifying these leakage errors using such anappropriate method enables the interrelation equations (A6a) to (A6d) tobe rearranged into the following interrelation equations (A7a) to (A7d).Such substitution of the variables simplifies the equations, so thatdescription below will be made after the substitution.

[Numerical Formula 20]

S _(21W) =S _(21M) −E _(XF2)  (A7a)

S _(12W) =S _(12M) −E _(XR2)  (A7b)

S _(21V) =S _(21D) −E _(XF1)  (A7c)

S _(12V) =S _(12D) −E _(XR1)  (A7d)

The remaining 24 undetermined coefficients constitute right-sidefractional sections of the equations, and the interrelation equations(A6a) to (A6d) are basically rational expressions, so that at least oneof coefficients including in numerators and denominators can bearbitrarily determined. For example, it is assumed that both a₀ and b₀be one, and when the equations are arranged to be vectorial equations,the interrelation equations (A6a) to (A6d) are further rearranged intothe following interrelation equations (A8a) to (A8d). Symbol t in theinterrelation equations (A8a) to (A8d) indicates a vector, in which rowsare replaced with lines. $\begin{matrix}{\left\lbrack {{Numerical}\quad {Formula}\quad 21} \right\rbrack \quad} & \quad \\{{\left( {{{- S_{11D}}*_{{S12W}^{*}}S_{21W}} - {S_{11D}*S_{11M}} - {S_{11D}*S_{22M}} - {S_{11D}S_{11M}*S_{22M}S_{12W}*S_{21W}S_{11M}S_{22M}1}} \right)\begin{pmatrix}a_{1} & a_{2} & a_{3} & a_{4} & c_{0} & c_{1} & c_{2} & c_{3} & c_{4}\end{pmatrix}^{t}} = {S_{11D}*S_{11M}*S_{22M}}} & ({A8a}) \\{{\left( {{{- S_{21V}}*S_{12W}*S_{21W}} - {S_{21V}*S_{11M}} - {S_{21V}*S_{22M}} - {S_{21V}S_{21W}*S_{22M}S_{21W}}} \right)\begin{pmatrix}a_{1} & a_{2} & a_{3} & a_{4} & d_{0} & d_{1}\end{pmatrix}^{t}} = {S_{21V}*S_{11M}*S_{22M}}} & ({A8b}) \\{{\left( {{{- S_{12V}}*S_{12W}*S_{21W}} - {S_{12V}*S_{11M}} - {S_{12V}*S_{22M}} - {S_{12V}S_{12W}*S_{11M}S_{12W}}} \right)\begin{pmatrix}b_{1} & b_{2} & b_{3} & b_{4} & e_{0} & e_{1}\end{pmatrix}^{t}} = {S_{12V}*S_{11M}*S_{22M}}} & ({A8c}) \\{{\left( {{{- S_{22D}}*S_{12W}*S_{21W}} - {S_{22D}*S_{11M}} - {S_{22D}*S_{22M}} - {S_{22D}S_{11M}*S_{22M}S_{12W}*S_{21W}S_{11M}S_{22M}1}} \right)\begin{pmatrix}b_{1} & b_{2} & b_{3} & b_{4} & f_{0} & f_{1} & f_{2} & f_{3} & f_{4}\end{pmatrix}^{t}} = {S_{22D}*S_{11M}*S_{22M}}} & ({A8d})\end{matrix}$

It is noteworthy that the sample scattering coefficients (S_(11A),S_(21A), S_(12A), and S_(22A)) are not included in the interrelationequations (A8a) to (A8d), and 22 undetermined coefficients are onlyincluded therein. That is, measuring one correction-data acquisitionsample 11B with both the reference measuring system 1 (the measurementfixture 5A) and the actual measuring system 2 (the measurement fixture5B), we can obtain the interrelation equations (A8a) to (A8d).

Accordingly, measuring 5.5 (22/4, 6 actually) correction-dataacquisition samples 11B_(1 to 6) with both the reference measuringsystem 1 (the measurement fixture 5A) and the actual measuring system 2(the measurement fixture 5B) enables entire undetermined coefficients tobe determined using the interrelation equations (A8a) to (A8d).

As described above, when the leakage errors (E_(XF1), E_(XR1), E_(XF2),and E_(XR2)) are not eliminated, an additional one correction-dataacquisition sample 11B is required for measuring them, so that sevencorrection-data acquisition samples 11B, to 7 are needed in total.

After the undetermined coefficients are once identified, the valuesmeasured by the reference measuring system (the reference measurementfixture) can be calculated from the values of an arbitrary targetelectronic component 11A measured by the actual measuring system 2 (theactual measurement fixture 5B) using interrelation equations (A6a) to(A6d).

Determining the undetermined coefficients using the interrelationequations (A8a) to (A8d) may employ any method; however, it will take alot of trouble without a computer. An example of a determining method ofthe undetermined coefficients using a computer will be described.

First, the leakage errors (E_(XF1), E_(XR1), E_(XF2), and E_(XR2))inherent in the measuring systems 1 and 2 (the measurement fixtures 5Aand 5B) are determined by measuring the scattering coefficients in astate of the measurement fixtures 5A and 5B without having thecorrection-data acquisition samples 11B_(1 to 6) attached thereto. Then,continuously, characteristics (scattering coefficients) of appropriatelyproduced six correction-data acquisition samples 11B_(1 to 6) aremeasured with both the reference measuring system 1 (the referencemeasurement fixture 5A) and the actual measuring system 2 (the actualmeasurement fixture 5B). Thereby, six measured values of the respectivereference measuring system 1 and the actual measuring system 2 areobtained. The measured values of the correction-data acquisition samples11B_(1 to 6) are distinguished with final subscripts, such as S_(11D1),S_(11D2), . . . , S_(11D6), and S_(11M1), . . . , S_(11M6).

Next, the measured values of the correction-data acquisition samples11B_(1 to 6) are substituted in the interrelation equations (A8a) and(A8b), and the measured value of the correction-data acquisition sample11B₆ is substituted in the interrelation equation (A8a). The followingequation (A9) is obtained by rearranging these substituted equations ofthe measured values to be a determinant. $\begin{matrix}{\left\lbrack {{Numerical}\quad {Formula}\quad 22} \right\rbrack \quad ({A9})} \\{{\begin{pmatrix}{{- S_{11{D1}}}*S_{12{W1}}*S_{21{W1}}} & {{- S_{11{D1}}}*S_{11{M1}}} & {{- S_{11{D1}}}*S_{22{M1}}} & {- S_{11{D1}}} & {S_{11{M1}}*S_{22{M1}}} & {S_{12{W1}}*S_{21{W1}}} & S_{11{M1}} & S_{22{M1}} & 1 & 0 & 0 \\{{- S_{21{V1}}}*S_{12{W1}}*S_{21{W1}}} & {{- S_{21{V1}}}*S_{11{M1}}} & {{- S_{21{V1}}}*S_{22{M1}}} & {- S_{21{V1}}} & 0 & 0 & 0 & 0 & 0 & {S_{21{W1}}*S_{22{M1}}} & S_{21{W1}} \\{{- S_{11{D2}}}*S_{12{W2}}*S_{21{W2}}} & {{- S_{11{D2}}}*S_{11{M2}}} & {{- S_{11{D2}}}*S_{22{M2}}} & {- S_{11{D2}}} & {S_{11{M2}}*S_{22{M2}}} & {S_{12{W2}}*S_{21{W2}}} & S_{11{M2}} & S_{22{M2}} & 1 & 0 & 0 \\{{- S_{21{V2}}}*S_{12{W2}}*S_{21{W2}}} & {{- S_{21{V2}}}*S_{11{M2}}} & {{- S_{21{V2}}}*S_{22{M2}}} & {- S_{21{V2}}} & 0 & 0 & 0 & 0 & 0 & {S_{21{W2}}*S_{22{M2}}} & S_{21{W2}} \\{{- S_{11{D3}}}*S_{12{W3}}*S_{21{W3}}} & {{- S_{11{D3}}}*S_{11{M3}}} & {{- S_{11{D3}}}*S_{22{M3}}} & {- S_{11{D3}}} & {S_{11{M3}}*S_{22{M3}}} & {S_{12{W3}}*S_{21{W3}}} & S_{11{M3}} & S_{22{M3}} & 1 & 0 & 0 \\{{- S_{21{V3}}}*S_{12{W3}}*S_{21{W3}}} & {{- S_{21{V3}}}*S_{11{M3}}} & {{- S_{21{V3}}}*S_{22{M3}}} & {- S_{21{V3}}} & 0 & 0 & 0 & 0 & 0 & {S_{21{W3}}*S_{22{M3}}} & S_{21{W3}} \\{{- S_{11{D4}}}*S_{12{W4}}*S_{21{W4}}} & {{- S_{11{D4}}}*S_{11{M4}}} & {{- S_{11{D4}}}*S_{22{M4}}} & {- S_{11{D4}}} & {S_{11{M4}}*S_{22{M4}}} & {S_{12{W4}}*S_{21{W4}}} & S_{11{M4}} & S_{22{M4}} & 1 & 0 & 0 \\{{- S_{21{V4}}}*S_{12{W4}}*S_{21{W4}}} & {{- S_{21{V4}}}*S_{11{M4}}} & {{- S_{21{V4}}}*S_{22{M4}}} & {- S_{21{V4}}} & 0 & 0 & 0 & 0 & 0 & {S_{21{W4}}*S_{22{M4}}} & S_{21{W4}} \\{{- S_{11{D5}}}*S_{12{W5}}*S_{21{W5}}} & {{- S_{11{D5}}}*S_{11{M5}}} & {{- S_{11{D5}}}*S_{22{M5}}} & {- S_{11{D5}}} & {S_{511M}*S_{22{M5}}} & {S_{12{W5}}*S_{21{W5}}} & S_{11{M5}} & S_{22{M5}} & 1 & 0 & 0 \\{{- S_{21{V5}}}*S_{12{W5}}*S_{21{W5}}} & {{- S_{21{V5}}}*S_{11{M5}}} & {{- S_{21{V5}}}*S_{22{M5}}} & {- S_{21{V5}}} & 0 & 0 & 0 & 0 & 0 & {S_{21{W5}}*S_{22{M5}}} & S_{21{W5}} \\{{- S_{11{D6}}}*S_{12{W6}}*S_{21{W6}}} & {{- S_{11{D6}}}*S_{11{M6}}} & {{- S_{11{D6}}}*S_{22{M6}}} & {- S_{11{D6}}} & {S_{11{M6}}*S_{22{M6}}} & {S_{12{W6}}*S_{21{W6}}} & S_{11{M6}} & S_{22{M6}} & 1 & 0 & 0\end{pmatrix}*\begin{pmatrix}a_{1} \\a_{2} \\a_{3} \\a_{4} \\c_{0} \\c_{1} \\c_{2} \\c_{3} \\c_{4} \\d_{0} \\d_{1}\end{pmatrix}} = \begin{pmatrix}{S_{11{D1}}*S_{11{M1}}*S_{22{M1}}} \\{S_{21{V1}}*S_{11{M1}}*S_{22{M1}}} \\{S_{11{D2}}*S_{11{M2}}*S_{22{M2}}} \\{S_{21{V2}}*S_{11{M2}}*S_{22{M2}}} \\{S_{11{D3}}*S_{11{M3}}*S_{22{M3}}} \\{S_{21{V3}}*S_{11{M3}}*S_{22{M3}}} \\{S_{11{D4}}*S_{11{M4}}*S_{22{M4}}} \\{S_{21{V4}}*S_{11{M4}}*S_{22{M4}}} \\{S_{11{D5}}*S_{11{M5}}*S_{22{M5}}} \\{S_{21{V5}}*S_{11{M5}}*S_{22{M5}}} \\{S_{11{D6}}*S_{11{M6}}*S_{22{M6}}}\end{pmatrix}}\end{matrix}$

Since factors of coefficient matrices and right-side constant termvectors in the equation (A9) are all known, the equation (A9) is only aneleven-system coupled linear equation with regard to the undeterminedcoefficients (a₁ to a₄, c₀ to c₄, d₀, and d₁). It is easy to solve thisequation by a computer to obtain the determined coefficients using aknown algorithm such as LU decomposition and Gaussian elimination.Similarly, from the interrelation equations (A8c) and (A8d),undetermined coefficients (b₁ to b₄, e₀ to e₄, f₀, and f₁) can beobtained.

Since the leakage error is comparatively simply identified in manycases, according to this embodiment described above, the leakage errorsare individually identified at first, and then, the difference betweenthe values measured by the reference measuring system 1 and the actualmeasuring system 2, which is caused by effects of the remaining errors,is corrected using the correction-data acquisition samples 11B_(1 to 6).Alternatively, the difference between the values measured by thereference measuring system 1 and the actual measuring system 2, whichalso includes the leakage errors, may be corrected using thecorrection-data acquisition samples 11B_(1 to 6).

According to the present invention, the two-port measuring system isdescribed; however, a one-port and three-or-more-port measuring systemmay be of course incorporated in the present invention.

According to this embodiment, the generally used two-port error model(signal transfer pattern) is described; however, a different error model(signal transfer pattern) may be of course incorporated in the presentinvention corresponding to a measuring system such as a fixture.

In the interrelation equations (A4a) to (A4d), if the error factors ofthe reference measuring system 1 (the measurement fixture 5A) are valuesof a measuring system absolutely without having errors, that is, whenE_(XF)=0, E_(XR)=0, E_(DF)=0, E_(DR)=0, E_(RF)=1, E_(RR)=1, E_(SF)=0,E_(SR)=0, E_(TF)=1, E_(TR)=1, E_(LF)=0, and E_(LR)=0, the interrelationequations (A4a) to (A4d) agree with the theoretical equations (A1a) to(A1d). It is understood from the above that the generally used two-portcorrection method corresponds to a specific case (the reference fixtureis ideal) of the relative correction method according to thisembodiment.

According to this embodiment, the present invention has been describedin detail by recognizing the error factors of the reference measuringsystem 1 (the measurement fixture 5A) and the actual measuring system 2(the measurement fixture 5B); alternatively, a combination of the errorfactors of the measurement fixtures 5A and 5B and the error factors ofthe measuring systems 1 and 2 and measurement cable may be considered asone error factor. In this case, the signal transfer pattern (errormodel) also is directly realized based on the theoretical equations(A1a) to (A1d).

Therefore, from the measured values obtained from a noncalibrated actualmeasuring system having an actual measurement fixture attached thereto,the values that would be measured by a calibrated reference measuringsystem having a reference measurement fixture attached thereto can alsobe precisely obtained.

Other than the determining method of the undetermined factors accordingto this embodiment, additional several correction-data acquisitionsamples 11B are measured in advance, and by using these measured values,the undetermined factors may also be determined with amaximum-likelihood method represented by a least-squares method. Suchdetermination can reduce the effect of measuring errors during samplemeasurement.

Except for the leakage, by four correction-data acquisition samples 11B,coefficients of the correction equations of the analytical relativecorrection method should be normally determined; however, according tothis embodiment, 5.5 (6, actually) correction-data acquisition samples11B_(1 to 6) are used therefor. This is a method conveniently adoptedfor simplifying the equations.

However, in determining factors using 5.5 correction-data acquisitionsamples 11B_(1 to 6), there are cases where the relationship betweenfactors to be satisfied with each other cannot be satisfied because ofthe effect of measurement errors of the correction-data acquisitionsamples. For example, in comparing the interrelation equations (A5a) to(A5d) with the interrelation equations (A6a) to (A6d), the relationshipa₁/a₃=c₄/c₃ should be satisfied; however, factors to satisfy suchrelationship may not be obtained depending to the measurement.

In such a case, the factors can be modified into more precise ones byrepetitive computations using the measured results of the fourcorrection-data acquisition samples 11B_(1 to 4) as evaluation functionsand the coefficients obtained from the 5.5 correction-data acquisitionsamples 11B_(1 to 6) as initial values. This is because the initialvalue of a tentative solution can be easily converged in the true valueby the Newton's method as long as the initial value is close to the truevalue.

The description above is the principle of the relative correction methodin the two-port measurement system. Next, the design of thecorrection-data acquisition sample 11B will be described. In performingthe relative correction method, it is a very important problem for thecorrection accuracy how to generate the correction-data acquisitionsamples 11B. If the correction-data acquisition samples 11B can bemeasured without errors by the reference measuring system 1 (referencemeasurement fixture 5A) and the actual measuring system 2 (actualmeasurement fixture 5B), respectively, coefficients of the correctionequation in the analytical relative correction method are determineddirectly and exclusively, as long as left-side matrices in the equation(A9) mentioned above do not become peculiar.

However, in the measurement of the correction-data acquisition samples11B, some errors (including both a systematic error and accidentalerror) are practically generated by all means. Thereby, an error isgenerated in coefficients of the correction equation in the analyticalrelative correction method obtained by the equation (A9).

In the coefficient errors generated in such a manner, the magnitude ofthe effect is different depending on the kind of the scatteringcoefficient in the correction-data acquisition samples 11B. For example,one of conditions that are assumed to have the least effect of thecorrection-data acquisition samples 11B is the case in that theleft-side matrix in the equation (A9) comes close to an identity matrix.In addition, in practice, the equation (A9 is operated by applying anidea such as a least squares method not using the equation as it is; theabove conditions are also the same in this case.

It will be described below that the correction equation in theanalytical relative correction method is produced to be difficult beingaffected by the measurement errors by the design of the correction-dataacquisition samples 11B. It is assumed here to produce thecorrection-data acquisition samples 11B by mainly combining resistors.This is for simplifying the production of the correction-dataacquisition samples 11B.

In order to produce the correction equation in the analytical relativecorrection method at a high accuracy, the followings are important: thereliability in calculation of coefficients of the correction equation;characteristic proximity between the prepared plural correction-dataacquisition samples 11B; and characteristic dependency between theprepared plural correction-data acquisition samples 11B.

First, the condition in that coefficients of the correction equation inthe analytical relative correction method can be securely calculatedwill be described. Using two correction-data acquisition samples 11Bhaving entirely the same characteristics means that the number ofcorrection-data acquisition samples 11B is reduced by one. Therefore, itis easily understood that this is one of the conditions in which thecorrection coefficients cannot be calculated. This condition can also bemathematically and simply expressed. That is, the left-side determinantvalue of the equation (A9) is zero. Thus, the correction coefficientscannot be calculated. Therefore, as long as the reverse condition thatthe left-side determinant value of the equation (A9) does not becomezero is satisfied, a solution exists in the equation (A9).

However, the condition that the left-side determinant value of theequation (A9) does not become zero is too abstract for designing thecorrection-data acquisition samples 11B. Therefore, according to thisembodiment, the following measures are used. Although the measure isslightly inaccurate, for practical purposes, there is no problem in sucha simple method (a method using the measure) because it scarcely occursthat the determinant value becomes zero.

A first measure is that the following calculated values determined bythe designed scattering coefficients of the correction-data acquisitionsamples 11B do not become extremely small or similar in the entirecorrection-data acquisition samples 11B. The calculated values are S₁₁,S₂₁, S₁₂, S₂₂, S₁₁*S₂₂, S₂₁*S₁₂, S₂₁*S₂₂, S₁₂*S₁₁, S₁₁*S₂₁*S₁₂,S₂₂*S₂₁*S₁₂. In the measure, these calculated values constitute matrixelements corresponding to the respective coefficients, and if the firstmeasure is satisfied, the matrix may approach zero.

A second measure is that the inequality of the calculated valuesmentioned above for each of the correction-data acquisition samples 11Bis to not to be common to each other as small as possible. This measureis based on the fact that if the inequality is different, the matrix maynot approach zero.

By satisfying the measures mentioned above, coefficients of thecorrection equations of the analytical relative correction method can besecurely calculated.

Next, the characteristic proximity between the prepared pluralcorrection-data acquisition samples 11B will be described. In theanalytical relative correction method according to the presentinvention, the measurement errors affecting the method cannot beavoided. In order to suppress such an effect of the measurement errors,it is important that the characteristic proximity between the preparedplural correction-data acquisition samples 11B is separated as far aspossible, which will be described below.

In the measurement of the correction-data acquisition samples 11B, someerrors are generated by all means even if the samples are carefullymeasured. These errors include all errors such as positioning errorswhen the correction-data acquisition samples 11B are attached to themeasurement fixtures 5A and 5B and measurement drifts or dispersion ofthe measuring systems 1 and 2.

The method is largely affected by errors whet at least twocorrection-data acquisition samples 11B have extremely closecharacteristics. This is easily understood from the fact that thedifferential coefficient of the correction-data acquisition samples 11Bin the vicinity of characteristics is give by a value of thecharacteristic difference between adjacent correction-data acquisitionsamples 11B divided by the characteristic distance (norm) of thecorrection-data acquisition samples 11B. That is, when a divisor issmall, a micro-error of a dividend is expanded.

Therefore, in order to suppress the effect of the measurement errors, itis effective that the norm between characteristics of thecorrection-data acquisition samples 11B is maintained as large aspossible. As the norm, a simple geometrical distance (a square root ofthe squared sum of parameter differences of S₁₁ to S₂₂) may be used.

It is recognized here that when the correction-data acquisition samples11B are produced of only resistors, the characteristics thereof arenecessarily collected to a real axis and imaginary axial components arescarcely provided. As long as the measurement errors do not exist, evenwhen imaginary components are not provided in characteristics of thecorrection-data acquisition samples 11B, the imaginary components of theerror factors of the measurement fixtures 5A and 5B are principallyoverlapped, resulting in assuming precise correction coefficients(undetermined coefficients). However, there are cases where thecharacteristics of only some correction-data acquisition samples 11Bhave imaginary components. In this case, there is apprehension that acorrection coefficient (undetermined coefficient) is obtained, whichcauses the corrected results of the correction-data acquisition samples11B having phase rotation to have a large amount of errors. This isliable to become actualized especially in a device (such as an isolator)having scattering coefficients with phase angles being different inforward and backward directions.

When it is difficult to sufficiently reduce the amount of measurementerrors of the correction-data acquisition samples 11B (errors thatcannot be removed by averaging, such as drifts of the measuring systems1 and 2), the using of the correction-data acquisition samples 11B withdifferent phase angles is most effective. Specifically, this can beachieved by assembling a delay line and a reactance element such as acapacitor and inductor to the correction-data acquisition samples 11B.

In the target electronic component 11A having a phase angle beingdifferent from that of the correction-data acquisition samples 11B, itis also effective to use the target electronic component 11A itself asone of the correction-data acquisition samples 11B. However, in anymethods, the frequency bandwidth capable of being measured is limited tothe correction-data acquisition samples 11B. In the manner describedabove, the effect of the measurement error can be suppressed to aminimum.

Next, characteristic dependency between the prepared pluralcorrection-data acquisition samples 11B will be described. Theinterrelation equations (A6a) to (A6d) described above are equations forassuming the values to be measured by the reference measuring system 1(reference measurement fixture 5A) from the values measured by theactual measuring system 2 (actual measurement fixture 5B). Theseequations are simple rational expressions, and both the numerator anddenominator are scattering coefficients measured in the correction-dataacquisition samples 11B and linear combinations of the product of thecoefficients. Therefore, the linear dependence may be produced betweenterms, which will be described below.

For example, the interrelation equation (A6a), which is an estimatedequation of S_(11D), has a section c₂*S_(11M)+c₃*S_(22M) in thenumerator. If values are precisely assumed as c₂ and c₃ on the basis ofthe measured results of the correction-data acquisition samples 11B,precise correction can be performed by characteristic relativecorrection of any of the correction-data acquisition samples 11B.However, if the value of c₂ is extremely large or conversely, c₃ has asign opposite to c₂, there is possibility that each term of the sectionc₂*S_(11M)+c₃*S_(22M) is cancelled with each other, so that a look-likecorrected result of S_(11D) is obtained from the correction-dataacquisition samples 11B. Then, in a sample (the target electroniccomponent 11A) other than the correction-data acquisition samples 11B,an extremely large or small error value is assumed as S_(11D).

In order to avoid such a defect, a linearly dependent unrepresentablecombination may be added to the characteristics of the correction-dataacquisition samples 11B. As for the example of S₁₁ and S₂₂, the lineardependence is considered as S₁₁ increase and S₂₂ increase or as S₁₁increase and S₂₂ decrease. Therefore, in order to avoid the lineardependence, the correction-data acquisition samples 11B may be combinedso as to cause the following both cases:

(1) S₁₁ increase and S₂₂ increase

(2) S₁₁ increase and S₂₂ decrease.

Similarly, if the following cases are included, the linear dependencecannot occur from the S₂₂ side:

(3) S₁₁ decrease and S₂₂ increase

(4) S₁₁ decrease and S₂₂ decrease.

As characteristic combinations from the interrelation equations (A6a) to(A6d), in which the linear dependence occurs, there are combinations ofS₁₁*S₂₂ and S₂₁*S₁₂ other than S₁₁ and S₂₂. Therefore, for thesecombinations, the characteristic design of the correction-dataacquisition samples 11B may also be performed paying attention to thesimilar points described above.

The measurement error correction method according to this embodimentwill be specifically described below.

The prepared six correction-data acquisition samples 11B_(1 to 6) aremounted on the reference measuring system 1. Then, electricalcharacteristics of the correction-data acquisition samples 11B_(1 to 6)are measured for each frequency point. The SAW filter corresponding tothe correction-data acquisition samples 11B_(1 to 6) is a high-frequencyelectronic component, and the electrical characteristic to be measuredhere is an S parameter comprising a scattering coefficient S₁₁ in theforward direction, scattering coefficient S₂₁ in the forward direction,scattering coefficient S₁₂ in the backward direction, and scatteringcoefficient S₂₂ in the backward direction.

The measured results (S₁₁ ^(n*), S₂₁ ^(n*), S₁₂ ^(n*), and S₂₂ ^(n*): n:natural numbers of 1 to 6) of the S parameter of the correction-dataacquisition samples 11B_(1 to 6) on the reference measuring system 1 areinput in the actual measuring system 2 via a data input unit thereof(not shown) in advance. The input results (S₁₁ ^(n*), S₂₁ ^(n*), S₁₂^(n*), and S₂₂ ^(n*)) measured by the reference measuring system 1 arestored in the memory 23 via the control unit body 22.

On the other hand, similarly, the correction-data acquisition samples11B_(1 to 6) are also mounted on the actual measuring system 2. Then,electrical characteristics of the correction-data acquisition samples11B_(1 to 6) are measured for each frequency point.

The measured results (S₁₁ ^(nM), S₂₁ ^(nM), S₁₂ ^(nM), and S₂₂ ^(nM): n:natural numbers of 1 to 6) of the S parameter of the correction-dataacquisition samples 11B_(1 to 6) on the actual measuring system 2 areinput in the interrelating formula computing means 24 via the controlunit body 22.

After the results (S₁₁ ^(nM), S₂₁ ^(nM), S₁₂ ^(nM), and S₂₂ ^(nM)) ofthe correction-data acquisition samples 11B_(1 to 6) measured by theactual measuring system 2 are input, the interrelating formula computingmeans 24 reads out the results (S₁₁ ^(n*), S₂₁ ^(n*), S₁₂ ^(n*), and S₂₂^(n*)) measured by the reference measuring system 1 from the memory 23via the control unit body 22.

The interrelating formula computing means 24 computes the interrelationequations between the results measured by the actual measuring system 2and the results measured by the reference measuring system 1 on thebasis of the measured results (S₁₁ ^(nM), S₂₁ ^(nM), S₁₂ ^(nM), and S₂₂^(nM)) and the measured results (S₁₁ ^(n*), S₂₁ ^(n*), S₁₂ ^(n*), andS₂₂ ^(n*)). The computing method has been described in detail above withreference to the theoretical equations (A1a to A1d), (A2a to A2d), and(A3a to A3d) and the interrelation equations (A4a to A4d), (A5a to A5d),(A6a to A6d), (A7a to A7d), (A8a to A8d), and (A9), so that thedescription thereof is omitted.

After the preliminary process described above, electricalcharacteristics (the S parameter S₁₁ ^(M), S₂₁ ^(M), S₁₂ ^(M), and S₂₂^(M)) of the target electronic component 11A are measured by the networkanalyzer body 20 in the actual measuring system 2. The measured resultsof the target electronic component 11A are input in the correcting means25 via the control unit body 22.

After the measured results of the target electronic component 11A areinput, the correcting means 25 reads out the interrelation equationsfrom the memory 23 via the control unit body 22. The correcting means 25substitutes the electrical characteristics (the S parameter S₁₁ ^(M),S₂₁ ^(M), S₁₂ ^(M), and S₂₂ ^(M)), which are the measured results of thetarget electronic component 11A, into the interrelation equations so asto be computed. Thereby, the correcting means 25 corrects the measuredresults (electrical characteristics) of the target electronic component11A on the actual measuring system 2 to the electrical characteristics(S₁₁*, S₂₁*, S₁₂*, and S₂₂*), which are assumed to be obtained whenbeing measured by the reference measuring system 1. The correcting means25 outputs the computed corrected values outsides via the control unitbody 22. The output may be displayed on a display unit (not shown) ormay be output by a data output unit (not shown) as data.

In addition, this computation process, as described above, may beperformed by the control unit 21 built in the network analyzer 3B, orthe measured results may be output to an outside computer connected tothe network analyzer 3B so as to allow the outside computer to performthe computation process.

The specific results corrected by the two-port correction methodaccording to this embodiment from the electrical characteristics of thetarget electronic component 11A (two-port) measured by the actualmeasuring system 2 (actual measurement fixture 5B) will be describedwith reference to FIGS. 8 to 10.

As the reference measurement fixture 5A, a so-called substrate forquality assurance to users having conductive rubber putted thereon isused. As the actual measurement fixture 5B, the reference measurementfixture 5A having a two pF capacitor attached thereto to purposely causea large error factor therein is used. As the correction-data acquisitionsample 11B, an isolator package having a chip resistor attached theretois used. FIG. 8 shows the corrected results of the scatteringcoefficient in the forward direction; FIG. 9 is a partial enlargeddrawing of the corrected results of the scattering coefficient in theforward direction; and FIG. 10 shows the corrected results of thescattering coefficient in the backward direction.

As understood from these drawings, if the correction method according tothis embodiment is performed, the large measurement difference betweenthe actual measuring system 2 (the measurement fixture 5B) and thereference measuring system 1 (the measurement fixture 5A) issubstantially precisely corrected. That is, the corrected results areobtained by the relative correction method based on the actual, and ifthe corrected results agree with “the value measured by the actualmeasurement”, it is shown that the correction is normally performed, andwhich is practically performed. In referring to FIG. 9, which is partialenlarged, it is apparent to be substantially precisely corrected.

The following point in the measurement data also is noteworthy. That is,although the correction-data acquisition samples 11B are apparentlynondirectional devices because they are entirely made of resistors, therelative correction of the target electronic component 11A beingapparently directional such as an isolator can be performed in highaccuracy. This comes from the following reason. Since S21 and S12 in theequation (A9) are not in the temporary connecting relationship, therelative correction coefficients can be entirely identified withoutusing the directional device as the correction-data acquisition sample11B. Thereby, the relative correction of the target electronic component11A made of the nondirectional device can also be performed in highaccuracy.

This has the following advantage. That is, manufacturing thecorrection-data acquisition sample 11B made of the directional devicewith a broad band is extremely difficult, so that it is very importantin practically performing the relative correction method not to requiresuch a correction-data acquisition sample 11B. However, since the targetelectronic component 11A is liable to be weak to measurement errors,when the target electronic component 11A has a high directionalcharacter such as an isolator, one of the devices itself may bepractically used as the correction-data acquisition sample 11B.

The above description is of the case in which this embodiment isperformed in the unbalanced two-port measurement system. Next, is thecase in which this embodiment is performed in an unbalanced one-portmeasurement system will be described.

The error factors in the measurement systems (the reference measuringsystem 1 and the actual measuring system 2) are modeled by the signaltransfer pattern shown in FIG. 11. The signal transfer pattern shown inFIG. 11 is the same as a generally used one-port error model.

In this signal transfer pattern, if the error factors are entirelyidentified, the scattering coefficient true value S_(11A) of thecorrection-data acquisition samples 11B can be obtained from themeasured value S_(11M) thereof according to the following theoreticalequations (A10a) and (A10b). The theoretical equations (A10a) and (A10b)can be derived from the signal transfer pattern shown in FIG. 11.$\begin{matrix}\left\lbrack {{Numerical}\quad {Formula}\quad 23} \right\rbrack & \quad \\{S_{11A} = \frac{S_{11M} - a}{{c\quad S_{11M}} + b - {a\quad c}}} & \text{(A10a)} \\{S_{11A} = \frac{S_{11D} - a^{\prime}}{{c^{\prime}\quad S_{11D}} + b^{\prime} - {a^{\prime}\quad c^{\prime}}}} & \text{(A10b)}\end{matrix}$

When the correction-data acquisition samples 11B, in which thescattering coefficient true value is (S_(11A)), is measured, thescattering coefficient S_(11D) is measured in the reference measuringsystem 1 and the scattering coefficient S_(11M) is measured in theactual measuring system 2.

It is practically impossible to specifically know the scatteringcoefficient true value S_(11A) of the correction-data acquisitionsamples 11B and error factor values of the reference measuring system 1(the measurement fixture 5A) and the actual measuring system 2 (themeasurement fixture 5B). On the other hand, the value S_(11D) measuredby the reference measuring system 1 and the value S_(11M) measured bythe actual measuring system 2 can be known by actual measurement.

It is an object of the relative correction method according to thisembodiment to obtain the value measured by the reference measuringsystem 1 from the value measured by the actual measuring system 2.

In comparison of the theoretical equation (A10a) with the theoreticalequation (A10b), the left-side members are the same scatteringcoefficient true value S_(11A). Therefore, the following equation (A11)can be derived from these theoretical equations (A10a) and (A10b).$\begin{matrix}\left\lbrack {{Numerical}\quad {Formula}\quad 24} \right\rbrack & \quad \\{\frac{S_{11D} - a^{\prime}}{{c^{\prime}\quad S_{11D}} + b^{\prime} - {a^{\prime}\quad c^{\prime}}} = \frac{S_{11M} - a}{{c\quad S_{11M}} + b - {a\quad c}}} & \text{(A11)}\end{matrix}$

Furthermore, by rearranging the equation (A11) with respect to S_(11D),the following interrelation equation (A12) can be derived. Theinterrelation equation (A12) is an equation showing the relationshipbetween the results measured by the actual measuring system 2 and theresults measured by the reference measuring system 1. $\begin{matrix}\left\lbrack {{Numerical}\quad {Formula}\quad 25} \right\rbrack & \quad \\{S_{11D} = \frac{{\left( {{a^{\prime}c^{\prime}} - {a^{\prime}\quad c} - b^{\prime}} \right)S_{11M}} - {a\quad a^{\prime}\quad c^{\prime}} + {a\quad a^{\prime}\quad c} + {a\quad b^{\prime}} - {a^{\prime}\quad b}}{{\left( {c^{\prime} - c} \right)S_{11M}} - {a\quad c^{\prime}} + {a\quad c} - b}} & \text{(A12)}\end{matrix}$

In the interrelation equation (A12), if the error factors of thereference measuring system 1 (the measurement fixture 5A) are values ofa measuring system entirely without errors, i.e., a′=0, b′=0, and c′=0,the following equation (A13) is derived from the interrelation equation(A12). This equation (A13) agrees with the theoretical equations (A10a)and (A10b). It is understood from the above that the generally usedone-port correction method corresponds to a specific case (the referencefixture is ideal) of the relative correction method according to thisembodiment. $\begin{matrix}\left\lbrack {{Numerical}\quad {Formula}\quad 26} \right\rbrack & \quad \\{S_{11D} = \frac{S_{11M} - a}{{c\quad S_{11M}} - {a\quad c} + b}} & \text{(A13)}\end{matrix}$

At the sight of the interrelation equation (A12) in detail,(−aa′c′+aa′c+ab′+a′b), (c−c′), and (−ac′+ac−b), which constitute theinterrelation equation (A12), can be substituted for one undeterminedcoefficient, respectively. Then, if these sections are substituted forundetermined coefficients α, β, and χ, respectively, the interrelationequation (A12) can be rearranged to the following interrelation equation(A14). $\begin{matrix}\left\lbrack {{Numerical}\quad {Formula}\quad 27} \right\rbrack & \quad \\{S_{11D} = \frac{S_{11M} + \alpha}{{\beta \quad S_{11M}} + \gamma}} & \text{(A14)}\end{matrix}$

Furthermore, since three unknown quantities α, β, and χ exist in theinterrelation equation (A14), three correction-data acquisition samplesare prepared to measure the respective characteristics, so that thesequantities can be identified. Then, using the same codes as those of thetwo-port allows leading the interrelation equations (A15a to A15c).$\begin{matrix}{\left\lbrack {{Numerical}\quad {Formula}\quad 28} \right\rbrack \quad} & \quad \\{a = \frac{\begin{matrix}{- \left( {S_{11{N1}}\left( {{S_{11{M1}}\left( {{S_{11{M3}}S_{11{N2}}} - {S_{11{M2}}S_{11{N3}}}} \right)} +} \right.} \right.} \\{\left. {{S_{11{M2}}S_{11{M3}}S_{11{N3}}} - {S_{11{M2}}S_{11{M3}}S_{11{N2}}}} \right) +} \\\left. {S_{11{M1}}{S_{11{N2}}\left( {{S_{11{M2}}S_{11{N3}}} - {S_{11{M3}}S_{11{N3}}}} \right)}} \right)\end{matrix}}{\begin{matrix}{S_{11{N1}}\left( {{S_{11{M2}}S_{11{N3}}} + {S_{11{M1}}\left( {S_{11{N2}} - S_{11{N3}}} \right)} -} \right.} \\{\left. {S_{11{M2}}S_{11{N2}}} \right) + {S_{11{N2}}\left( {{S_{11{M2}}S_{11{N3}}} - {S_{11{M3}}S_{11{N3}}}} \right)}}\end{matrix}}} & \text{(A15a)} \\{\beta = \frac{\begin{matrix}{- \left( {{S_{11{M1}}\left( {S_{11{N3}} - S_{11{N2}}} \right)} - {S_{11{M2}}S_{11{N3}}} +} \right.} \\\left. {{S_{11{M3}}S_{11{N2}}} + {\left( {S_{11{M2}} - S_{11{M3}}} \right)S_{11{N1}}}} \right)\end{matrix}}{\begin{matrix}{S_{11{N1}}\left( {{S_{11{M2}}S_{11{N3}}} + {S_{11{M1}}\left( {S_{11{N2}} - S_{11{N3}}} \right)} -} \right.} \\{\left. {S_{11{M2}}S_{11{N2}}} \right) + {S_{11{N2}}\left( {{S_{11{M2}}S_{11{N3}}} - {S_{11{M3}}S_{11{N3}}}} \right)}}\end{matrix}}} & \text{(A15b)} \\{\gamma = \frac{\begin{matrix}{{S_{11{M1}}\left( {{S_{11{M3}}S_{11{D3}}} - {S_{11{M2}}S_{11{D2}}}} \right)} - {S_{11{M2}}S_{11{M3}}S_{11{D3}}} +} \\{{S_{11{M2}}S_{11{M3}}S_{11{D2}}} + {S_{11{M1}}{S_{11{D1}}\left( {S_{11{M2}} - S_{11{M3}}} \right)}}}\end{matrix}}{\begin{matrix}{S_{11{D1}}\left( {{S_{11{M2}}S_{11{D3}}} + {S_{11{M1}}\left( {S_{11{D2}} - S_{11{D3}}} \right)} -} \right.} \\{\left. {S_{11{M2}}S_{11{D2}}} \right) + {S_{11{D2}}\left( {{S_{11{M2}}S_{11{D3}}} - {S_{11{M3}}S_{11{D3}}}} \right)}}\end{matrix}}} & \text{(A15c)}\end{matrix}$

On the basis of the interrelation equations (A15a to A15c), if threecorrection-data acquisition samples 11B_(1 to 3) are prepared to measurethe respective characteristics, undetermined coefficients (relativecorrection coefficients) α, β, and χ can be identified.

The practical correcting operation of measured values performed afteridentification of the undetermined coefficients as described above isthe same as in the correcting operation of the two-port measuringsystem, so that the description thereof is omitted.

The specific results of electrical characteristics of the targetelectronic component 11A (one-port) measured by the actual measuringsystem 2 (the measurement fixture 5B) and further corrected by thetwo-port relative correction method according to this embodiment will bedescribed with reference to FIG. 12.

As is apparent from FIG. 12, according to the correction method of thisembodiment, even in a one-port electronic component, it is understoodthat a large measured value difference between the actual measuringsystem 2 (the actual measurement fixture 5B) and the reference measuringsystem 1 (the reference measurement fixture 5A) is substantiallyprecisely corrected. That is, the corrected results are obtained fromthe values measured by the actual measuring system shown in the graph.If the corrected results agree with the values measured by the referencemeasuring system, the correction is normally performed, and it isperformed in that way in fact.

The correction method of measured results according to this embodimentdescribed above has the following advantages. That is, in assuringcharacteristics of electronic components by manufacturers of thecomponents, the electrical characteristics are assured on the basis ofthe results measured by a measuring system arranged in the manufacturer.However, it is not necessarily to have the same results when theelectrical characteristics are measured by a measuring system arrangedin a user who has bought the components. Therefore, the characteristicsassured by the manufacturer cannot be confirmed, resulting in uncertainassurance without repeatability.

Whereas, when the measuring system in the manufacturer side is to be thereference measuring system while the measuring system in the user sideis to be the actual measuring system, if the correction method ofmeasurement errors according to this embodiment is performed, theelectrical characteristics assumed to be the same as the measuredresults in the manufacturer side can be calculated by the user on thebasis of the results measured by the measuring system in the user side.Thereby, the assurance of electronic components by the manufacturer canbe repeated and sufficiently secured, enabling the assurance to bereceived by the user.

Moreover, the correction described above can be performed without strictinspection of the actual measuring system 2 (characteristics of themeasurement fixture 5B of the actual measuring system 2 are adjusted tobe identical to those of the measurement fixture 5A of the referencemeasuring system 1, for example.), so that the cost required for themeasurement can be suppressed that much.

Furthermore, in the user side, many automatic measuring and sortingmachines installed in a mass production line can also be selected as theactual measuring systems, so that the cost required for the measurement(defective-component sorting cost, in this case) can be furthersuppressed that much, while the measuring time is reduced.

Moreover, not only measurement errors due to the measurement fixtures 5Aand 5B but also measurement errors of the entire actual measuring systemcan be simultaneously corrected, so that calibration such as the fulltwo-port correction method need not be performed in the actual measuringsystem 2, further suppressing measuring cost that much.

Furthermore, in the measuring system according to this embodiment, evenwhen the actual measuring system 5B is used, in which the performancefor being incorporated into an automatic measuring and sorting machineand the long life are given priority over stabilizing measurementcharacteristics, measured results cannot be affected therefrom, so thatthe cost required for the measurement can be further suppressed thatmuch, while the measuring time is reduced.

Second Embodiment

According to a second embodiment, a measurement error correction methodis incorporated in the present invention, in which selecting asurface-mount SAW filter as a target electronic component, electricalcharacteristics of the SAW filter are measured by a measuring systemhaving a network analyzer. According to the second embodiment, measuredvalues are corrected by an approximate-relative correction method thatis only different from the first embodiment. Therefore, arrangements ofthe measuring systems 1 and 2 and measurement fixtures 5A and 5B are thesame as those of the first embodiment, so that device arrangements ofthe first embodiment are correspondingly applied to this embodiment andthe description thereof is omitted.

First, a plurality of (five, for example) correction-data acquisitionsamples 11B_(1 to 5) are prepared. The prepared five correction-dataacquisition samples 11B_(1 to 5) are mounted on the reference measuringsystem 1. Then, electrical characteristics of the correction-dataacquisition samples 11B_(1 to 5) are measured for each frequency point.The SAW filter corresponding to the correction-data acquisition samples11B_(1 to 5) is a high-frequency electronic component, and theelectrical characteristic to be measured here is an S parametercomprising a scattering coefficient S₁₁ in the forward direction,scattering coefficient S₂₁ in the forward direction, scatteringcoefficient S₁₂ in the backward direction, and scattering coefficientS₂₂ in the backward direction.

The measured results (S₁₁ ^(n*), _(S) ₂₁ ^(n*), S₁₂ ^(n*), and S₂₂^(n*): n: natural numbers of 1 to 5) of the S parameter of thecorrection-data acquisition samples 11B_(1 to 5) on the referencemeasuring system 1 are input in the actual measuring system 2 via a datainput unit thereof (not shown) in advance. The input results (S₁₁ ^(n*),S₂₁ ^(n*), S₁₂ ^(n*), and S₂₂ ^(n*)) measured by the reference measuringsystem 1 are stored in the memory 23 via the control unit body 22.

On the other hand, similarly, the correction-data acquisition samples11B_(1 to 5) are also mounted on the actual measuring system 2. Then,electrical characteristics of the correction-data acquisition samples11B_(1 to 5) are measured for each frequency point.

The measured results (S₁₁ ^(nM), S₂₁ ^(nM), S₁₂ ^(nM), and S₂₂ ^(nM): n:natural numbers of 1 to 5) of the S parameter of the correction-dataacquisition samples 11B_(1 to 5) on the actual measuring system 2 areinput in the interrelating formula computing means 24 via the controlunit body 22.

After the results (S₁₁ ^(nM), S₂₁ ^(nM), S₁₂ ^(nM), and S₂₂ ^(nM)) ofthe correction-data acquisition samples 11B_(1 to 5) measured by theactual measuring system 2 are input, the interrelating formula computingmeans 24 reads out the results (S₁₁ ^(n*), S₂₁ ^(n*), S₁₂ ^(n*), and S₂₂^(n*)) measured by the reference measuring system 1 from the memory 23via the control unit body 22.

The interrelating formula computing means 24 stores an interrelationequation approximately showing the relationship between the resultsmeasured by the actual measuring system and the results measured by thereference measuring system and undetermined-coefficient computingequations. The interrelation equation is formed of the following linearexpression (B2) and comprises undetermined coefficients (a_(m), b_(m),e_(m), and d_(m): m; integers of 0 to 4). The undetermined-coefficientcomputing equations are formed of the following equations (B1a) to(B1d). The undetermined-coefficient computing equations (B1a) to (B1d)are for computing undetermined coefficients (a_(m), b_(m), c_(m), andd_(m): m; integers of 0 to 4) and are generated based on theinterrelation equation (B2). $\begin{matrix}\left\lbrack {{Numerical}\quad {Formula}\quad 1} \right\rbrack & \quad \\{\begin{pmatrix}S_{11}^{1^{*}} \\S_{11}^{2^{*}} \\S_{11}^{3^{*}} \\S_{11}^{4^{*}} \\S_{11}^{5^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & 1\end{pmatrix}\begin{pmatrix}a_{1} \\a_{2} \\a_{3} \\a_{4} \\a_{0}\end{pmatrix}}} & \text{B1a} \\{\begin{pmatrix}S_{21}^{1^{*}} \\S_{21}^{2^{*}} \\S_{21}^{3^{*}} \\S_{21}^{4^{*}} \\S_{21}^{5^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & 1\end{pmatrix}\begin{pmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4} \\b_{0}\end{pmatrix}}} & \text{B1b} \\{\begin{pmatrix}S_{12}^{1^{*}} \\S_{12}^{2^{*}} \\S_{12}^{3^{*}} \\S_{12}^{4^{*}} \\S_{12}^{5^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & 1\end{pmatrix}\begin{pmatrix}c_{1} \\c_{2} \\c_{3} \\c_{4} \\c_{0}\end{pmatrix}}} & \text{B1c} \\{\begin{pmatrix}S_{22}^{1^{*}} \\S_{22}^{2^{*}} \\S_{22}^{3^{*}} \\S_{22}^{4^{*}} \\S_{22}^{5^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & 1\end{pmatrix}\begin{pmatrix}d_{1} \\d_{2} \\d_{3} \\d_{4} \\d_{0}\end{pmatrix}}} & \text{B1d} \\\left\lbrack {{Numerical}\quad {Formula}\quad 2} \right\rbrack & \quad \\{\begin{pmatrix}S_{11}^{*} \\S_{21}^{*} \\S_{12}^{*} \\S_{22}^{*}\end{pmatrix} = {{\begin{pmatrix}a_{1} & a_{2} & a_{3} & a_{4} \\b_{1} & b_{2} & b_{3} & b_{4} \\c_{1} & c_{2} & c_{3} & c_{4} \\d_{1} & d_{2} & d_{3} & d_{4}\end{pmatrix}\begin{pmatrix}S_{11}^{M} \\S_{21}^{M} \\S_{12}^{M} \\S_{22}^{M}\end{pmatrix}} + \begin{pmatrix}a_{0} \\b_{0} \\c_{0} \\d_{0}\end{pmatrix}}} & \text{B2}\end{matrix}$

S₁₁*, S₂₁*, S₁₂*, and S₂₂*: the S parameter of the target electroniccomponent 11A assumed to be obtained by the reference measuring system1.

S₁₁ ^(M), S₂₁ ^(M), S₁₂ ^(M), and S₂₂ ^(M): the S parameter of thetarget electronic component 11A measured by the actual measuring system2.

The interrelating formula computing means 24 determines the undeterminedcoefficients (a_(m), b_(m), c_(m), and d_(m): m; integers of 0 to 4) bysubstituting both measured results, which are the S parameter (S₁₁^(nM), S₂₁ ^(nM), S₁₂ ^(nM), and S₂₂ ^(nM)) and the S parameter (S₁₁^(n*), S₂₁ ^(n*), S₁₂ ^(n*), and S₂₂ ^(n*)), in theundetermined-coefficient computing equations (B1a) to (B1d).

The interrelating formula computing means 24 determines theinterrelation equation between the results measured by the actualmeasuring system 2 and the results measured by the reference measuringsystem 1 by inserting the identified undetermined coefficients (a_(m),b_(m), c_(m), and d_(m)) into the interrelation equation (B2). Theinterrelation equation is determined for each frequency point. Thedetermined interrelation equation is input and recorded in the memory 23by the interrelating formula computing means 24 via the control unitbody 22.

After the preliminary process described above, electricalcharacteristics (the S parameter S₁₁ ^(M), S₂₁ ^(M), S₁₂ ^(M), and S₂₂^(M)) of the target electronic component 11A are measured by the networkanalyzer body 20 in the actual measuring system 2. The measured resultsof the target electronic component 11A are input in the correcting means25 via the control unit body 22.

After the measured results of the target electronic component 11A areinput, the correcting means 25 reads out the interrelation equationsfrom the memory 23 via the control unit body 22. The correcting means 25substitutes the electrical characteristics (the S parameter S₁₁ ^(M),S₂₁ ^(M), S₁₂ ^(M), and S₂₂ ^(M)), which are the measured results of thetarget electronic component 11A, into the interrelation equations so asto be computed. Thereby, the correcting means 25 corrects the measuredresults (electrical characteristics) of the target electronic component11A on the actual measuring system 2 to the electrical characteristics(S₁₁*, S₂₁*, S₁₂*, and S₂₂*), which are assumed to be obtained whenbeing measured by the reference measuring system 1. The correcting means25 outputs the computed corrected values outsides via the control unitbody 22. The output may be displayed on a display unit (not shown) ormay be output by a data output unit (not shown) as data.

In addition, this computation process, as described above, may beperformed by the control unit 21 built in the network analyzer 3B, orthe measured results may be output to an outside computer connected tothe network analyzer 3B so as to allow the outside computer to performthe computation process.

The correction method of measured results according to this embodimenthas the following advantages. That is, in assuring characteristics ofelectronic components by manufacturers of the components, the electricalcharacteristics are assured on the basis of the results measured by ameasuring system arranged in the manufacturer. However, it is notnecessarily to have the same results when the electrical characteristicsare measured by a measuring system arranged in a user who has bought thecomponents. Therefore, the characteristics assured by the manufacturercannot be confirmed, resulting in uncertain assurance withoutrepeatability.

Whereas, when the measuring system in the manufacturer side is to be thereference measuring system while the measuring system in the user sideis to be the actual measuring system, if the correction method ofmeasurement errors according to the embodiment is performed, theelectrical characteristics assumed to be the same as the measuredresults in the manufacturer side can be calculated by the user on thebasis of the results measured by the measuring system in the user side.Thereby, the assurance of electronic components by the manufacturer canbe repeated and sufficiently secured, enabling the assurance to bereceived by the user.

Moreover, the correction described above can be performed without strictinspection of the actual measuring system 2 (characteristics of themeasurement fixture 5B of the actual measuring system 2 are adjusted tobe identical to those of the measurement fixture 5A of the referencemeasuring system 1, for example.), so that the cost required for themeasurement can be suppressed that much.

Furthermore, in the user side, many automatic measuring and sortingmachines installed in a mass production line can also be selected as theactual measuring systems, so that the cost required for the measurement(defective-component sorting cost, in this case) can be furthersuppressed that much, while the measuring time is reduced.

Moreover, not only measurement errors due to the measurement fixtures 5Aand 5B but also measurement errors of the entire actual measuring systemcan be simultaneously corrected, so that calibration such as the fulltwo-port correction method need not be performed in the actual measuringsystem 2, further suppressing measuring cost that much.

Furthermore, in the measuring system according to this embodiment, evenwhen the actual measuring system 5B is used, in which the performancefor being incorporated into an automatic measuring and sorting machineand the long life are given priority over stabilizing measurementcharacteristics, measured results cannot be affected therefrom, so thatthe cost required for the measurement can be further suppressed thatmuch, while the measuring time is reduced.

Furthermore, in the measuring system (the approximate-relativecorrection method) according to this embodiment, nonlinear errors can becorrected.

Third Embodiment

The device arrangement for performing measured error correction methodaccording to a third embodiment is basically the same as that of thefirst and second embodiments, so that like reference charactersdesignate like elements common to each embodiment, and the descriptionthereof is omitted.

According to the embodiment, although the same correction method as thatof the second embodiment is performed, the computing method forperforming correction is slightly different from that of the secondembodiment. According to this embodiment, 15 samples 11B_(1 to 15) withelectrical characteristics, which are generated by measurement operationof the measuring system and being different from each other, areprepared as the correction-data acquisition samples 11B.

The prepared 15 correction-data acquisition sample 11B_(1 to 15) aremounted on the reference measuring system 1 and the actual measuringsystem 2 so as to measure the S parameter.

The interrelating formula computing means 24 stores interrelationequations approximately showing the relationship between the resultsmeasured by the actual measuring system and the results measured by thereference measuring system and undetermined-coefficient computingequations. The interrelation equations are formed of the followingquadratic expressions (C2a) to (c2d) and comprises undeterminedcoefficients (a_(q), b_(q), C_(q), and d_(q): q; integers of 0 to 14).The undetermined-coefficient computing equations are formed of thefollowing equations (B1a) to (B1d). The undetermined-coefficientcomputing equations (C1a) to (C1d) are for computing undeterminedcoefficients (a_(q), b_(q), c_(q), and d_(q): q; integers of 0 to 14)and are generated based on the interrelation equations (C2a) to (c2d).$\begin{matrix}{\left\lbrack {{Numerical}\quad {Formula}\quad 3} \right\rbrack \quad {C1a}} \\{\begin{pmatrix}S_{11}^{1^{*}} \\S_{11}^{2^{*}} \\S_{11}^{3^{*}} \\S_{11}^{4^{*}} \\S_{11}^{5^{*}} \\S_{11}^{6^{*}} \\S_{11}^{7^{*}} \\S_{11}^{8^{*}} \\S_{11}^{9^{*}} \\S_{11}^{10^{*}} \\S_{11}^{11^{*}} \\S_{11}^{12^{*}} \\S_{11}^{13^{*}} \\S_{11}^{14^{*}} \\S_{11}^{15^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & \left( S_{11}^{1M} \right)^{2} & \left( S_{21}^{1M} \right)^{2} & \left( S_{12}^{1M} \right)^{2} & \left( S_{22}^{1M} \right)^{2} & {S_{11}^{1M}S_{21}^{1M}} & {S_{11}^{1M}S_{12}^{1M}} & {S_{11}^{1M}S_{22}^{1M}} & {S_{21}^{1M}S_{12}^{1M}} & {S_{21}^{1M}S_{22}^{1M}} & {S_{12}^{1M}S_{22}^{1M}} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & \left( S_{11}^{2M} \right)^{2} & \left( S_{21}^{2M} \right)^{2} & \left( S_{12}^{2M} \right)^{2} & \left( S_{22}^{2M} \right)^{2} & {S_{11}^{2M}S_{21}^{2M}} & {S_{11}^{2M}S_{12}^{2M}} & {S_{11}^{2M}S_{22}^{2M}} & {S_{21}^{2M}S_{12}^{2M}} & {S_{21}^{2M}S_{22}^{2M}} & {S_{12}^{2M}S_{22}^{2M}} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & \left( S_{11}^{3M} \right)^{2} & \left( S_{21}^{3M} \right)^{2} & \left( S_{12}^{3M} \right)^{2} & \left( S_{22}^{3M} \right)^{2} & {S_{11}^{3M}S_{21}^{3M}} & {S_{11}^{3M}S_{12}^{3M}} & {S_{11}^{3M}S_{22}^{3M}} & {S_{21}^{3M}S_{12}^{3M}} & {S_{21}^{3M}S_{22}^{3M}} & {S_{12}^{3M}S_{22}^{3M}} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & \left( S_{11}^{4M} \right)^{2} & \left( S_{21}^{4M} \right)^{2} & \left( S_{12}^{4M} \right)^{2} & \left( S_{22}^{4M} \right)^{2} & {S_{11}^{4M}S_{21}^{4M}} & {S_{11}^{4M}S_{12}^{4M}} & {S_{11}^{4M}S_{22}^{4M}} & {S_{21}^{4M}S_{12}^{4M}} & {S_{21}^{4M}S_{22}^{4M}} & {S_{12}^{4M}S_{22}^{4M}} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & \left( S_{11}^{5M} \right)^{2} & \left( S_{21}^{5M} \right)^{2} & \left( S_{12}^{5M} \right)^{2} & \left( S_{22}^{5M} \right)^{2} & {S_{11}^{5M}S_{21}^{5M}} & {S_{11}^{5M}S_{12}^{5M}} & {S_{11}^{5M}S_{22}^{5M}} & {S_{21}^{5M}S_{12}^{5M}} & {S_{21}^{5M}S_{22}^{5M}} & {S_{12}^{5M}S_{22}^{5M}} & 1 \\S_{11}^{6M} & S_{21}^{6M} & S_{12}^{6M} & S_{22}^{6M} & \left( S_{11}^{6M} \right)^{2} & \left( S_{21}^{6M} \right)^{2} & \left( S_{12}^{6M} \right)^{2} & \left( S_{22}^{6M} \right)^{2} & {S_{11}^{6M}S_{21}^{6M}} & {S_{11}^{6M}S_{12}^{6M}} & {S_{11}^{6M}S_{22}^{6M}} & {S_{21}^{6M}S_{12}^{6M}} & {S_{21}^{6M}S_{22}^{6M}} & {S_{12}^{6M}S_{22}^{6M}} & 1 \\S_{11}^{7M} & S_{21}^{7M} & S_{12}^{7M} & S_{22}^{7M} & \left( S_{11}^{7M} \right)^{2} & \left( S_{21}^{7M} \right)^{2} & \left( S_{12}^{7M} \right)^{2} & \left( S_{22}^{7M} \right)^{2} & {S_{11}^{7M}S_{21}^{7M}} & {S_{11}^{7M}S_{12}^{7M}} & {S_{11}^{7M}S_{22}^{7M}} & {S_{21}^{7M}S_{12}^{7M}} & {S_{21}^{7M}S_{22}^{7M}} & {S_{12}^{7M}S_{22}^{7M}} & 1 \\S_{11}^{8M} & S_{21}^{8M} & S_{12}^{8M} & S_{22}^{8M} & \left( S_{11}^{8M} \right)^{2} & \left( S_{21}^{8M} \right)^{2} & \left( S_{12}^{8M} \right)^{2} & \left( S_{22}^{8M} \right)^{2} & {S_{11}^{8M}S_{21}^{8M}} & {S_{11}^{8M}S_{12}^{8M}} & {S_{11}^{8M}S_{22}^{8M}} & {S_{21}^{8M}S_{12}^{8M}} & {S_{21}^{8M}S_{22}^{8M}} & {S_{12}^{8M}S_{22}^{8M}} & 1 \\S_{11}^{9M} & S_{21}^{9M} & S_{12}^{9M} & S_{22}^{9M} & \left( S_{11}^{9M} \right)^{2} & \left( S_{21}^{9M} \right)^{2} & \left( S_{12}^{9M} \right)^{2} & \left( S_{22}^{9M} \right)^{2} & {S_{11}^{9M}S_{21}^{9M}} & {S_{11}^{9M}S_{12}^{9M}} & {S_{11}^{9M}S_{22}^{9M}} & {S_{21}^{9M}S_{12}^{9M}} & {S_{21}^{9M}S_{22}^{9M}} & {S_{12}^{9M}S_{22}^{9M}} & 1 \\S_{11}^{10M} & S_{21}^{10M} & S_{12}^{10M} & S_{22}^{10M} & \left( S_{11}^{10M} \right)^{2} & \left( S_{21}^{10M} \right)^{2} & \left( S_{12}^{10M} \right)^{2} & \left( S_{22}^{10M} \right)^{2} & {S_{11}^{10M}S_{21}^{10M}} & {S_{11}^{10M}S_{12}^{10M}} & {S_{11}^{10M}S_{22}^{10M}} & {S_{21}^{10M}S_{12}^{10M}} & {S_{21}^{10M}S_{22}^{10M}} & {S_{12}^{10M}S_{22}^{10M}} & 1 \\S_{11}^{11M} & S_{21}^{11M} & S_{12}^{11M} & S_{22}^{11M} & \left( S_{11}^{11M} \right)^{2} & \left( S_{21}^{11M} \right)^{2} & \left( S_{12}^{11M} \right)^{2} & \left( S_{22}^{11M} \right)^{2} & {S_{11}^{11M}S_{21}^{11M}} & {S_{11}^{11M}S_{12}^{11M}} & {S_{11}^{11M}S_{22}^{11M}} & {S_{21}^{11M}S_{12}^{11M}} & {S_{21}^{11M}S_{22}^{11M}} & {S_{12}^{11M}S_{22}^{11M}} & 1 \\S_{11}^{12M} & S_{21}^{12M} & S_{12}^{12M} & S_{22}^{12M} & \left( S_{11}^{12M} \right)^{2} & \left( S_{21}^{12M} \right)^{2} & \left( S_{12}^{12M} \right)^{2} & \left( S_{22}^{12M} \right)^{2} & {S_{11}^{12M}S_{21}^{12M}} & {S_{11}^{12M}S_{12}^{12M}} & {S_{11}^{12M}S_{22}^{12M}} & {S_{21}^{12M}S_{12}^{12M}} & {S_{21}^{12M}S_{22}^{12M}} & {S_{12}^{12M}S_{22}^{12M}} & 1 \\S_{11}^{13M} & S_{21}^{13M} & S_{12}^{13M} & S_{22}^{13M} & \left( S_{11}^{13M} \right)^{2} & \left( S_{21}^{13M} \right)^{2} & \left( S_{12}^{13M} \right)^{2} & \left( S_{22}^{13M} \right)^{2} & {S_{11}^{13M}S_{21}^{13M}} & {S_{11}^{13M}S_{12}^{13M}} & {S_{11}^{13M}S_{22}^{13M}} & {S_{21}^{13M}S_{12}^{13M}} & {S_{21}^{13M}S_{22}^{13M}} & {S_{12}^{13M}S_{22}^{13M}} & 1 \\S_{11}^{14M} & S_{21}^{14M} & S_{12}^{14M} & S_{22}^{14M} & \left( S_{11}^{14M} \right)^{2} & \left( S_{21}^{14M} \right)^{2} & \left( S_{12}^{14M} \right)^{2} & \left( S_{22}^{14M} \right)^{2} & {S_{11}^{14M}S_{21}^{14M}} & {S_{11}^{14M}S_{12}^{14M}} & {S_{11}^{14M}S_{22}^{14M}} & {S_{21}^{14M}S_{12}^{14M}} & {S_{21}^{14M}S_{22}^{14M}} & {S_{12}^{14M}S_{22}^{14M}} & 1 \\S_{11}^{15M} & S_{21}^{15M} & S_{12}^{15M} & S_{22}^{15M} & \left( S_{11}^{15M} \right)^{2} & \left( S_{21}^{15M} \right)^{2} & \left( S_{12}^{15M} \right)^{2} & \left( S_{22}^{15M} \right)^{2} & {S_{11}^{15M}S_{21}^{15M}} & {S_{11}^{15M}S_{12}^{15M}} & {S_{11}^{15M}S_{22}^{15M}} & {S_{21}^{15M}S_{12}^{15M}} & {S_{21}^{15M}S_{22}^{15M}} & {S_{12}^{15M}S_{22}^{15M}} & 1\end{pmatrix}\begin{pmatrix}a_{1} \\a_{2} \\a_{3} \\a_{4} \\a_{5} \\a_{6} \\a_{7} \\a_{8} \\a_{9} \\a_{10} \\a_{11} \\a_{12} \\a_{13} \\a_{14} \\a_{0}\end{pmatrix}}} \\{\left\lbrack {{Numerical}\quad {Formula}\quad 4} \right\rbrack \quad {C1b}} \\{\begin{pmatrix}S_{21}^{1^{*}} \\S_{21}^{2^{*}} \\S_{21}^{3^{*}} \\S_{21}^{4^{*}} \\S_{21}^{5^{*}} \\S_{21}^{6^{*}} \\S_{21}^{7^{*}} \\S_{21}^{8^{*}} \\S_{21}^{9^{*}} \\S_{21}^{10^{*}} \\S_{21}^{11^{*}} \\S_{21}^{12^{*}} \\S_{21}^{13^{*}} \\S_{21}^{14^{*}} \\S_{21}^{15^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & \left( S_{11}^{1M} \right)^{2} & \left( S_{21}^{1M} \right)^{2} & \left( S_{12}^{1M} \right)^{2} & \left( S_{22}^{1M} \right)^{2} & {S_{11}^{1M}S_{21}^{1M}} & {S_{11}^{1M}S_{12}^{1M}} & {S_{11}^{1M}S_{22}^{1M}} & {S_{21}^{1M}S_{12}^{1M}} & {S_{21}^{1M}S_{22}^{1M}} & {S_{12}^{1M}S_{22}^{1M}} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & \left( S_{11}^{2M} \right)^{2} & \left( S_{21}^{2M} \right)^{2} & \left( S_{12}^{2M} \right)^{2} & \left( S_{22}^{2M} \right)^{2} & {S_{11}^{2M}S_{21}^{2M}} & {S_{11}^{2M}S_{12}^{2M}} & {S_{11}^{2M}S_{22}^{2M}} & {S_{21}^{2M}S_{12}^{2M}} & {S_{21}^{2M}S_{22}^{2M}} & {S_{12}^{2M}S_{22}^{2M}} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & \left( S_{11}^{3M} \right)^{2} & \left( S_{21}^{3M} \right)^{2} & \left( S_{12}^{3M} \right)^{2} & \left( S_{22}^{3M} \right)^{2} & {S_{11}^{3M}S_{21}^{3M}} & {S_{11}^{3M}S_{12}^{3M}} & {S_{11}^{3M}S_{22}^{3M}} & {S_{21}^{3M}S_{12}^{3M}} & {S_{21}^{3M}S_{22}^{3M}} & {S_{12}^{3M}S_{22}^{3M}} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & \left( S_{11}^{4M} \right)^{2} & \left( S_{21}^{4M} \right)^{2} & \left( S_{12}^{4M} \right)^{2} & \left( S_{22}^{4M} \right)^{2} & {S_{11}^{4M}S_{21}^{4M}} & {S_{11}^{4M}S_{12}^{4M}} & {S_{11}^{4M}S_{22}^{4M}} & {S_{21}^{4M}S_{12}^{4M}} & {S_{21}^{4M}S_{22}^{4M}} & {S_{12}^{4M}S_{22}^{4M}} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & \left( S_{11}^{5M} \right)^{2} & \left( S_{21}^{5M} \right)^{2} & \left( S_{12}^{5M} \right)^{2} & \left( S_{22}^{5M} \right)^{2} & {S_{11}^{5M}S_{21}^{5M}} & {S_{11}^{5M}S_{12}^{5M}} & {S_{11}^{5M}S_{22}^{5M}} & {S_{21}^{5M}S_{12}^{5M}} & {S_{21}^{5M}S_{22}^{5M}} & {S_{12}^{5M}S_{22}^{5M}} & 1 \\S_{11}^{6M} & S_{21}^{6M} & S_{12}^{6M} & S_{22}^{6M} & \left( S_{11}^{6M} \right)^{2} & \left( S_{21}^{6M} \right)^{2} & \left( S_{12}^{6M} \right)^{2} & \left( S_{22}^{6M} \right)^{2} & {S_{11}^{6M}S_{21}^{6M}} & {S_{11}^{6M}S_{12}^{6M}} & {S_{11}^{6M}S_{22}^{6M}} & {S_{21}^{6M}S_{12}^{6M}} & {S_{21}^{6M}S_{22}^{6M}} & {S_{12}^{6M}S_{22}^{6M}} & 1 \\S_{11}^{7M} & S_{21}^{7M} & S_{12}^{7M} & S_{22}^{7M} & \left( S_{11}^{7M} \right)^{2} & \left( S_{21}^{7M} \right)^{2} & \left( S_{12}^{7M} \right)^{2} & \left( S_{22}^{7M} \right)^{2} & {S_{11}^{7M}S_{21}^{7M}} & {S_{11}^{7M}S_{12}^{7M}} & {S_{11}^{7M}S_{22}^{7M}} & {S_{21}^{7M}S_{12}^{7M}} & {S_{21}^{7M}S_{22}^{7M}} & {S_{12}^{7M}S_{22}^{7M}} & 1 \\S_{11}^{8M} & S_{21}^{8M} & S_{12}^{8M} & S_{22}^{8M} & \left( S_{11}^{8M} \right)^{2} & \left( S_{21}^{8M} \right)^{2} & \left( S_{12}^{8M} \right)^{2} & \left( S_{22}^{8M} \right)^{2} & {S_{11}^{8M}S_{21}^{8M}} & {S_{11}^{8M}S_{12}^{8M}} & {S_{11}^{8M}S_{22}^{8M}} & {S_{21}^{8M}S_{12}^{8M}} & {S_{21}^{8M}S_{22}^{8M}} & {S_{12}^{8M}S_{22}^{8M}} & 1 \\S_{11}^{9M} & S_{21}^{9M} & S_{12}^{9M} & S_{22}^{9M} & \left( S_{11}^{9M} \right)^{2} & \left( S_{21}^{9M} \right)^{2} & \left( S_{12}^{9M} \right)^{2} & \left( S_{22}^{9M} \right)^{2} & {S_{11}^{9M}S_{21}^{9M}} & {S_{11}^{9M}S_{12}^{9M}} & {S_{11}^{9M}S_{22}^{9M}} & {S_{21}^{9M}S_{12}^{9M}} & {S_{21}^{9M}S_{22}^{9M}} & {S_{12}^{9M}S_{22}^{9M}} & 1 \\S_{11}^{10M} & S_{21}^{10M} & S_{12}^{10M} & S_{22}^{10M} & \left( S_{11}^{10M} \right)^{2} & \left( S_{21}^{10M} \right)^{2} & \left( S_{12}^{10M} \right)^{2} & \left( S_{22}^{10M} \right)^{2} & {S_{11}^{10M}S_{21}^{10M}} & {S_{11}^{10M}S_{12}^{10M}} & {S_{11}^{10M}S_{22}^{10M}} & {S_{21}^{10M}S_{12}^{10M}} & {S_{21}^{10M}S_{22}^{10M}} & {S_{12}^{10M}S_{22}^{10M}} & 1 \\S_{11}^{11M} & S_{21}^{11M} & S_{12}^{11M} & S_{22}^{11M} & \left( S_{11}^{11M} \right)^{2} & \left( S_{21}^{11M} \right)^{2} & \left( S_{12}^{11M} \right)^{2} & \left( S_{22}^{11M} \right)^{2} & {S_{11}^{11M}S_{21}^{11M}} & {S_{11}^{11M}S_{12}^{11M}} & {S_{11}^{11M}S_{22}^{11M}} & {S_{21}^{11M}S_{12}^{11M}} & {S_{21}^{11M}S_{22}^{11M}} & {S_{12}^{11M}S_{22}^{11M}} & 1 \\S_{11}^{12M} & S_{21}^{12M} & S_{12}^{12M} & S_{22}^{12M} & \left( S_{11}^{12M} \right)^{2} & \left( S_{21}^{12M} \right)^{2} & \left( S_{12}^{12M} \right)^{2} & \left( S_{22}^{12M} \right)^{2} & {S_{11}^{12M}S_{21}^{12M}} & {S_{11}^{12M}S_{12}^{12M}} & {S_{11}^{12M}S_{22}^{12M}} & {S_{21}^{12M}S_{12}^{12M}} & {S_{21}^{12M}S_{22}^{12M}} & {S_{12}^{12M}S_{22}^{12M}} & 1 \\S_{11}^{13M} & S_{21}^{13M} & S_{12}^{13M} & S_{22}^{13M} & \left( S_{11}^{13M} \right)^{2} & \left( S_{21}^{13M} \right)^{2} & \left( S_{12}^{13M} \right)^{2} & \left( S_{22}^{13M} \right)^{2} & {S_{11}^{13M}S_{21}^{13M}} & {S_{11}^{13M}S_{12}^{13M}} & {S_{11}^{13M}S_{22}^{13M}} & {S_{21}^{13M}S_{12}^{13M}} & {S_{21}^{13M}S_{22}^{13M}} & {S_{12}^{13M}S_{22}^{13M}} & 1 \\S_{11}^{14M} & S_{21}^{14M} & S_{12}^{14M} & S_{22}^{14M} & \left( S_{11}^{14M} \right)^{2} & \left( S_{21}^{14M} \right)^{2} & \left( S_{12}^{14M} \right)^{2} & \left( S_{22}^{14M} \right)^{2} & {S_{11}^{14M}S_{21}^{14M}} & {S_{11}^{14M}S_{12}^{14M}} & {S_{11}^{14M}S_{22}^{14M}} & {S_{21}^{14M}S_{12}^{14M}} & {S_{21}^{14M}S_{22}^{14M}} & {S_{12}^{14M}S_{22}^{14M}} & 1 \\S_{11}^{15M} & S_{21}^{15M} & S_{12}^{15M} & S_{22}^{15M} & \left( S_{11}^{15M} \right)^{2} & \left( S_{21}^{15M} \right)^{2} & \left( S_{12}^{15M} \right)^{2} & \left( S_{22}^{15M} \right)^{2} & {S_{11}^{15M}S_{21}^{15M}} & {S_{11}^{15M}S_{12}^{15M}} & {S_{11}^{15M}S_{22}^{15M}} & {S_{21}^{15M}S_{12}^{15M}} & {S_{21}^{15M}S_{22}^{15M}} & {S_{12}^{15M}S_{22}^{15M}} & 1\end{pmatrix}\begin{pmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4} \\b_{5} \\b_{6} \\b_{7} \\b_{8} \\b_{9} \\b_{10} \\b_{11} \\b_{12} \\b_{13} \\b_{14} \\b_{0}\end{pmatrix}}} \\{\left\lbrack {{Numerical}\quad {Formula}\quad 5} \right\rbrack \quad {C1c}} \\{\begin{pmatrix}S_{12}^{1^{*}} \\S_{12}^{2^{*}} \\S_{12}^{3^{*}} \\S_{12}^{4^{*}} \\S_{12}^{5^{*}} \\S_{12}^{6^{*}} \\S_{12}^{7^{*}} \\S_{12}^{8^{*}} \\S_{12}^{9^{*}} \\S_{12}^{10^{*}} \\S_{12}^{11^{*}} \\S_{12}^{12^{*}} \\S_{12}^{13^{*}} \\S_{12}^{14^{*}} \\S_{12}^{15^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & \left( S_{11}^{1M} \right)^{2} & \left( S_{21}^{1M} \right)^{2} & \left( S_{12}^{1M} \right)^{2} & \left( S_{22}^{1M} \right)^{2} & {S_{11}^{1M}S_{21}^{1M}} & {S_{11}^{1M}S_{12}^{1M}} & {S_{11}^{1M}S_{22}^{1M}} & {S_{21}^{1M}S_{12}^{1M}} & {S_{21}^{1M}S_{22}^{1M}} & {S_{12}^{1M}S_{22}^{1M}} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & \left( S_{11}^{2M} \right)^{2} & \left( S_{21}^{2M} \right)^{2} & \left( S_{12}^{2M} \right)^{2} & \left( S_{22}^{2M} \right)^{2} & {S_{11}^{2M}S_{21}^{2M}} & {S_{11}^{2M}S_{12}^{2M}} & {S_{11}^{2M}S_{22}^{2M}} & {S_{21}^{2M}S_{12}^{2M}} & {S_{21}^{2M}S_{22}^{2M}} & {S_{12}^{2M}S_{22}^{2M}} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & \left( S_{11}^{3M} \right)^{2} & \left( S_{21}^{3M} \right)^{2} & \left( S_{12}^{3M} \right)^{2} & \left( S_{22}^{3M} \right)^{2} & {S_{11}^{3M}S_{21}^{3M}} & {S_{11}^{3M}S_{12}^{3M}} & {S_{11}^{3M}S_{22}^{3M}} & {S_{21}^{3M}S_{12}^{3M}} & {S_{21}^{3M}S_{22}^{3M}} & {S_{12}^{3M}S_{22}^{3M}} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & \left( S_{11}^{4M} \right)^{2} & \left( S_{21}^{4M} \right)^{2} & \left( S_{12}^{4M} \right)^{2} & \left( S_{22}^{4M} \right)^{2} & {S_{11}^{4M}S_{21}^{4M}} & {S_{11}^{4M}S_{12}^{4M}} & {S_{11}^{4M}S_{22}^{4M}} & {S_{21}^{4M}S_{12}^{4M}} & {S_{21}^{4M}S_{22}^{4M}} & {S_{12}^{4M}S_{22}^{4M}} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & \left( S_{11}^{5M} \right)^{2} & \left( S_{21}^{5M} \right)^{2} & \left( S_{12}^{5M} \right)^{2} & \left( S_{22}^{5M} \right)^{2} & {S_{11}^{5M}S_{21}^{5M}} & {S_{11}^{5M}S_{12}^{5M}} & {S_{11}^{5M}S_{22}^{5M}} & {S_{21}^{5M}S_{12}^{5M}} & {S_{21}^{5M}S_{22}^{5M}} & {S_{12}^{5M}S_{22}^{5M}} & 1 \\S_{11}^{6M} & S_{21}^{6M} & S_{12}^{6M} & S_{22}^{6M} & \left( S_{11}^{6M} \right)^{2} & \left( S_{21}^{6M} \right)^{2} & \left( S_{12}^{6M} \right)^{2} & \left( S_{22}^{6M} \right)^{2} & {S_{11}^{6M}S_{21}^{6M}} & {S_{11}^{6M}S_{12}^{6M}} & {S_{11}^{6M}S_{22}^{6M}} & {S_{21}^{6M}S_{12}^{6M}} & {S_{21}^{6M}S_{22}^{6M}} & {S_{12}^{6M}S_{22}^{6M}} & 1 \\S_{11}^{7M} & S_{21}^{7M} & S_{12}^{7M} & S_{22}^{7M} & \left( S_{11}^{7M} \right)^{2} & \left( S_{21}^{7M} \right)^{2} & \left( S_{12}^{7M} \right)^{2} & \left( S_{22}^{7M} \right)^{2} & {S_{11}^{7M}S_{21}^{7M}} & {S_{11}^{7M}S_{12}^{7M}} & {S_{11}^{7M}S_{22}^{7M}} & {S_{21}^{7M}S_{12}^{7M}} & {S_{21}^{7M}S_{22}^{7M}} & {S_{12}^{7M}S_{22}^{7M}} & 1 \\S_{11}^{8M} & S_{21}^{8M} & S_{12}^{8M} & S_{22}^{8M} & \left( S_{11}^{8M} \right)^{2} & \left( S_{21}^{8M} \right)^{2} & \left( S_{12}^{8M} \right)^{2} & \left( S_{22}^{8M} \right)^{2} & {S_{11}^{8M}S_{21}^{8M}} & {S_{11}^{8M}S_{12}^{8M}} & {S_{11}^{8M}S_{22}^{8M}} & {S_{21}^{8M}S_{12}^{8M}} & {S_{21}^{8M}S_{22}^{8M}} & {S_{12}^{8M}S_{22}^{8M}} & 1 \\S_{11}^{9M} & S_{21}^{9M} & S_{12}^{9M} & S_{22}^{9M} & \left( S_{11}^{9M} \right)^{2} & \left( S_{21}^{9M} \right)^{2} & \left( S_{12}^{9M} \right)^{2} & \left( S_{22}^{9M} \right)^{2} & {S_{11}^{9M}S_{21}^{9M}} & {S_{11}^{9M}S_{12}^{9M}} & {S_{11}^{9M}S_{22}^{9M}} & {S_{21}^{9M}S_{12}^{9M}} & {S_{21}^{9M}S_{22}^{9M}} & {S_{12}^{9M}S_{22}^{9M}} & 1 \\S_{11}^{10M} & S_{21}^{10M} & S_{12}^{10M} & S_{22}^{10M} & \left( S_{11}^{10M} \right)^{2} & \left( S_{21}^{10M} \right)^{2} & \left( S_{12}^{10M} \right)^{2} & \left( S_{22}^{10M} \right)^{2} & {S_{11}^{10M}S_{21}^{10M}} & {S_{11}^{10M}S_{12}^{10M}} & {S_{11}^{10M}S_{22}^{10M}} & {S_{21}^{10M}S_{12}^{10M}} & {S_{21}^{10M}S_{22}^{10M}} & {S_{12}^{10M}S_{22}^{10M}} & 1 \\S_{11}^{11M} & S_{21}^{11M} & S_{12}^{11M} & S_{22}^{11M} & \left( S_{11}^{11M} \right)^{2} & \left( S_{21}^{11M} \right)^{2} & \left( S_{12}^{11M} \right)^{2} & \left( S_{22}^{11M} \right)^{2} & {S_{11}^{11M}S_{21}^{11M}} & {S_{11}^{11M}S_{12}^{11M}} & {S_{11}^{11M}S_{22}^{11M}} & {S_{21}^{11M}S_{12}^{11M}} & {S_{21}^{11M}S_{22}^{11M}} & {S_{12}^{11M}S_{22}^{11M}} & 1 \\S_{11}^{12M} & S_{21}^{12M} & S_{12}^{12M} & S_{22}^{12M} & \left( S_{11}^{12M} \right)^{2} & \left( S_{21}^{12M} \right)^{2} & \left( S_{12}^{12M} \right)^{2} & \left( S_{22}^{12M} \right)^{2} & {S_{11}^{12M}S_{21}^{12M}} & {S_{11}^{12M}S_{12}^{12M}} & {S_{11}^{12M}S_{22}^{12M}} & {S_{21}^{12M}S_{12}^{12M}} & {S_{21}^{12M}S_{22}^{12M}} & {S_{12}^{12M}S_{22}^{12M}} & 1 \\S_{11}^{13M} & S_{21}^{13M} & S_{12}^{13M} & S_{22}^{13M} & \left( S_{11}^{13M} \right)^{2} & \left( S_{21}^{13M} \right)^{2} & \left( S_{12}^{13M} \right)^{2} & \left( S_{22}^{13M} \right)^{2} & {S_{11}^{13M}S_{21}^{13M}} & {S_{11}^{13M}S_{12}^{13M}} & {S_{11}^{13M}S_{22}^{13M}} & {S_{21}^{13M}S_{12}^{13M}} & {S_{21}^{13M}S_{22}^{13M}} & {S_{12}^{13M}S_{22}^{13M}} & 1 \\S_{11}^{14M} & S_{21}^{14M} & S_{12}^{14M} & S_{22}^{14M} & \left( S_{11}^{14M} \right)^{2} & \left( S_{21}^{14M} \right)^{2} & \left( S_{12}^{14M} \right)^{2} & \left( S_{22}^{14M} \right)^{2} & {S_{11}^{14M}S_{21}^{14M}} & {S_{11}^{14M}S_{12}^{14M}} & {S_{11}^{14M}S_{22}^{14M}} & {S_{21}^{14M}S_{12}^{14M}} & {S_{21}^{14M}S_{22}^{14M}} & {S_{12}^{14M}S_{22}^{14M}} & 1 \\S_{11}^{15M} & S_{21}^{15M} & S_{12}^{15M} & S_{22}^{15M} & \left( S_{11}^{15M} \right)^{2} & \left( S_{21}^{15M} \right)^{2} & \left( S_{12}^{15M} \right)^{2} & \left( S_{22}^{15M} \right)^{2} & {S_{11}^{15M}S_{21}^{15M}} & {S_{11}^{15M}S_{12}^{15M}} & {S_{11}^{15M}S_{22}^{15M}} & {S_{21}^{15M}S_{12}^{15M}} & {S_{21}^{15M}S_{22}^{15M}} & {S_{12}^{15M}S_{22}^{15M}} & 1\end{pmatrix}\begin{pmatrix}c_{1} \\c_{2} \\c_{3} \\c_{4} \\c_{5} \\c_{6} \\c_{7} \\c_{8} \\c_{9} \\c_{10} \\c_{11} \\c_{12} \\c_{13} \\c_{14} \\c_{0}\end{pmatrix}}} \\{\left\lbrack {{Numerical}\quad {Formula}\quad 6} \right\rbrack \quad {C1d}} \\{\begin{pmatrix}S_{22}^{1^{*}} \\S_{22}^{2^{*}} \\S_{22}^{3^{*}} \\S_{22}^{4^{*}} \\S_{22}^{5^{*}} \\S_{22}^{6^{*}} \\S_{22}^{7^{*}} \\S_{22}^{8^{*}} \\S_{22}^{9^{*}} \\S_{22}^{10^{*}} \\S_{22}^{11^{*}} \\S_{22}^{12^{*}} \\S_{22}^{13^{*}} \\S_{22}^{14^{*}} \\S_{22}^{15^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{21}^{1M} & S_{12}^{1M} & S_{22}^{1M} & \left( S_{11}^{1M} \right)^{2} & \left( S_{21}^{1M} \right)^{2} & \left( S_{12}^{1M} \right)^{2} & \left( S_{22}^{1M} \right)^{2} & {S_{11}^{1M}S_{21}^{1M}} & {S_{11}^{1M}S_{12}^{1M}} & {S_{11}^{1M}S_{22}^{1M}} & {S_{21}^{1M}S_{12}^{1M}} & {S_{21}^{1M}S_{22}^{1M}} & {S_{12}^{1M}S_{22}^{1M}} & 1 \\S_{11}^{2M} & S_{21}^{2M} & S_{12}^{2M} & S_{22}^{2M} & \left( S_{11}^{2M} \right)^{2} & \left( S_{21}^{2M} \right)^{2} & \left( S_{12}^{2M} \right)^{2} & \left( S_{22}^{2M} \right)^{2} & {S_{11}^{2M}S_{21}^{2M}} & {S_{11}^{2M}S_{12}^{2M}} & {S_{11}^{2M}S_{22}^{2M}} & {S_{21}^{2M}S_{12}^{2M}} & {S_{21}^{2M}S_{22}^{2M}} & {S_{12}^{2M}S_{22}^{2M}} & 1 \\S_{11}^{3M} & S_{21}^{3M} & S_{12}^{3M} & S_{22}^{3M} & \left( S_{11}^{3M} \right)^{2} & \left( S_{21}^{3M} \right)^{2} & \left( S_{12}^{3M} \right)^{2} & \left( S_{22}^{3M} \right)^{2} & {S_{11}^{3M}S_{21}^{3M}} & {S_{11}^{3M}S_{12}^{3M}} & {S_{11}^{3M}S_{22}^{3M}} & {S_{21}^{3M}S_{12}^{3M}} & {S_{21}^{3M}S_{22}^{3M}} & {S_{12}^{3M}S_{22}^{3M}} & 1 \\S_{11}^{4M} & S_{21}^{4M} & S_{12}^{4M} & S_{22}^{4M} & \left( S_{11}^{4M} \right)^{2} & \left( S_{21}^{4M} \right)^{2} & \left( S_{12}^{4M} \right)^{2} & \left( S_{22}^{4M} \right)^{2} & {S_{11}^{4M}S_{21}^{4M}} & {S_{11}^{4M}S_{12}^{4M}} & {S_{11}^{4M}S_{22}^{4M}} & {S_{21}^{4M}S_{12}^{4M}} & {S_{21}^{4M}S_{22}^{4M}} & {S_{12}^{4M}S_{22}^{4M}} & 1 \\S_{11}^{5M} & S_{21}^{5M} & S_{12}^{5M} & S_{22}^{5M} & \left( S_{11}^{5M} \right)^{2} & \left( S_{21}^{5M} \right)^{2} & \left( S_{12}^{5M} \right)^{2} & \left( S_{22}^{5M} \right)^{2} & {S_{11}^{5M}S_{21}^{5M}} & {S_{11}^{5M}S_{12}^{5M}} & {S_{11}^{5M}S_{22}^{5M}} & {S_{21}^{5M}S_{12}^{5M}} & {S_{21}^{5M}S_{22}^{5M}} & {S_{12}^{5M}S_{22}^{5M}} & 1 \\S_{11}^{6M} & S_{21}^{6M} & S_{12}^{6M} & S_{22}^{6M} & \left( S_{11}^{6M} \right)^{2} & \left( S_{21}^{6M} \right)^{2} & \left( S_{12}^{6M} \right)^{2} & \left( S_{22}^{6M} \right)^{2} & {S_{11}^{6M}S_{21}^{6M}} & {S_{11}^{6M}S_{12}^{6M}} & {S_{11}^{6M}S_{22}^{6M}} & {S_{21}^{6M}S_{12}^{6M}} & {S_{21}^{6M}S_{22}^{6M}} & {S_{12}^{6M}S_{22}^{6M}} & 1 \\S_{11}^{7M} & S_{21}^{7M} & S_{12}^{7M} & S_{22}^{7M} & \left( S_{11}^{7M} \right)^{2} & \left( S_{21}^{7M} \right)^{2} & \left( S_{12}^{7M} \right)^{2} & \left( S_{22}^{7M} \right)^{2} & {S_{11}^{7M}S_{21}^{7M}} & {S_{11}^{7M}S_{12}^{7M}} & {S_{11}^{7M}S_{22}^{7M}} & {S_{21}^{7M}S_{12}^{7M}} & {S_{21}^{7M}S_{22}^{7M}} & {S_{12}^{7M}S_{22}^{7M}} & 1 \\S_{11}^{8M} & S_{21}^{8M} & S_{12}^{8M} & S_{22}^{8M} & \left( S_{11}^{8M} \right)^{2} & \left( S_{21}^{8M} \right)^{2} & \left( S_{12}^{8M} \right)^{2} & \left( S_{22}^{8M} \right)^{2} & {S_{11}^{8M}S_{21}^{8M}} & {S_{11}^{8M}S_{12}^{8M}} & {S_{11}^{8M}S_{22}^{8M}} & {S_{21}^{8M}S_{12}^{8M}} & {S_{21}^{8M}S_{22}^{8M}} & {S_{12}^{8M}S_{22}^{8M}} & 1 \\S_{11}^{9M} & S_{21}^{9M} & S_{12}^{9M} & S_{22}^{9M} & \left( S_{11}^{9M} \right)^{2} & \left( S_{21}^{9M} \right)^{2} & \left( S_{12}^{9M} \right)^{2} & \left( S_{22}^{9M} \right)^{2} & {S_{11}^{9M}S_{21}^{9M}} & {S_{11}^{9M}S_{12}^{9M}} & {S_{11}^{9M}S_{22}^{9M}} & {S_{21}^{9M}S_{12}^{9M}} & {S_{21}^{9M}S_{22}^{9M}} & {S_{12}^{9M}S_{22}^{9M}} & 1 \\S_{11}^{10M} & S_{21}^{10M} & S_{12}^{10M} & S_{22}^{10M} & \left( S_{11}^{10M} \right)^{2} & \left( S_{21}^{10M} \right)^{2} & \left( S_{12}^{10M} \right)^{2} & \left( S_{22}^{10M} \right)^{2} & {S_{11}^{10M}S_{21}^{10M}} & {S_{11}^{10M}S_{12}^{10M}} & {S_{11}^{10M}S_{22}^{10M}} & {S_{21}^{10M}S_{12}^{10M}} & {S_{21}^{10M}S_{22}^{10M}} & {S_{12}^{10M}S_{22}^{10M}} & 1 \\S_{11}^{11M} & S_{21}^{11M} & S_{12}^{11M} & S_{22}^{11M} & \left( S_{11}^{11M} \right)^{2} & \left( S_{21}^{11M} \right)^{2} & \left( S_{12}^{11M} \right)^{2} & \left( S_{22}^{11M} \right)^{2} & {S_{11}^{11M}S_{21}^{11M}} & {S_{11}^{11M}S_{12}^{11M}} & {S_{11}^{11M}S_{22}^{11M}} & {S_{21}^{11M}S_{12}^{11M}} & {S_{21}^{11M}S_{22}^{11M}} & {S_{12}^{11M}S_{22}^{11M}} & 1 \\S_{11}^{12M} & S_{21}^{12M} & S_{12}^{12M} & S_{22}^{12M} & \left( S_{11}^{12M} \right)^{2} & \left( S_{21}^{12M} \right)^{2} & \left( S_{12}^{12M} \right)^{2} & \left( S_{22}^{12M} \right)^{2} & {S_{11}^{12M}S_{21}^{12M}} & {S_{11}^{12M}S_{12}^{12M}} & {S_{11}^{12M}S_{22}^{12M}} & {S_{21}^{12M}S_{12}^{12M}} & {S_{21}^{12M}S_{22}^{12M}} & {S_{12}^{12M}S_{22}^{12M}} & 1 \\S_{11}^{13M} & S_{21}^{13M} & S_{12}^{13M} & S_{22}^{13M} & \left( S_{11}^{13M} \right)^{2} & \left( S_{21}^{13M} \right)^{2} & \left( S_{12}^{13M} \right)^{2} & \left( S_{22}^{13M} \right)^{2} & {S_{11}^{13M}S_{21}^{13M}} & {S_{11}^{13M}S_{12}^{13M}} & {S_{11}^{13M}S_{22}^{13M}} & {S_{21}^{13M}S_{12}^{13M}} & {S_{21}^{13M}S_{22}^{13M}} & {S_{12}^{13M}S_{22}^{13M}} & 1 \\S_{11}^{14M} & S_{21}^{14M} & S_{12}^{14M} & S_{22}^{14M} & \left( S_{11}^{14M} \right)^{2} & \left( S_{21}^{14M} \right)^{2} & \left( S_{12}^{14M} \right)^{2} & \left( S_{22}^{14M} \right)^{2} & {S_{11}^{14M}S_{21}^{14M}} & {S_{11}^{14M}S_{12}^{14M}} & {S_{11}^{14M}S_{22}^{14M}} & {S_{21}^{14M}S_{12}^{14M}} & {S_{21}^{14M}S_{22}^{14M}} & {S_{12}^{14M}S_{22}^{14M}} & 1 \\S_{11}^{15M} & S_{21}^{15M} & S_{12}^{15M} & S_{22}^{15M} & \left( S_{11}^{15M} \right)^{2} & \left( S_{21}^{15M} \right)^{2} & \left( S_{12}^{15M} \right)^{2} & \left( S_{22}^{15M} \right)^{2} & {S_{11}^{15M}S_{21}^{15M}} & {S_{11}^{15M}S_{12}^{15M}} & {S_{11}^{15M}S_{22}^{15M}} & {S_{21}^{15M}S_{12}^{15M}} & {S_{21}^{15M}S_{22}^{15M}} & {S_{12}^{15M}S_{22}^{15M}} & 1\end{pmatrix}\begin{pmatrix}d_{1} \\d_{2} \\d_{3} \\d_{4} \\d_{5} \\d_{6} \\d_{7} \\d_{8} \\d_{9} \\d_{10} \\d_{11} \\d_{12} \\d_{13} \\d_{14} \\d_{0}\end{pmatrix}}}\end{matrix}$

S₁₁ ^(p*), S₂₁ ^(p*), S₁₂ ^(p*), and S₂₂ ^(p*): the S parameter of thecorrection-data acquisition samples 11B_(1 to 15) measured by thereference measuring system 1

S₁₁ ^(pM), S₂₁ ^(pM), S₁₂ ^(pM), and S₂₂ ^(pM): the S parameter of thecorrection-data acquisition samples 11B_(1 to 5) measured by the actualmeasuring system 2 $\begin{matrix}{\left\lbrack {{Numerical}\quad {Formula}\quad 7} \right\rbrack \quad} & \quad \\{S_{11}^{*} = {\begin{pmatrix}a_{1} & a_{2} & a_{3} & a_{4} & a_{5} & a_{6} & a_{7} & a_{8} & a_{9} & a_{10} & a_{11} & a_{12} & a_{13} & a_{14} & a_{0}\end{pmatrix}\begin{pmatrix}S_{11}^{M} \\S_{21}^{M} \\S_{12}^{M} \\S_{22}^{M} \\\left( S_{11}^{M} \right)^{2} \\\left( S_{21}^{M} \right)^{2} \\\left( S_{12}^{M} \right)^{2} \\\left( S_{22}^{M} \right)^{2} \\{S_{11}^{M}S_{21}^{M}} \\{S_{11}^{M}S_{12}^{M}} \\{S_{11}^{M}S_{22}^{M}} \\{S_{21}^{M}S_{12}^{M}} \\{S_{21}^{M}S_{22}^{M}} \\{S_{12}^{M}S_{22}^{M}} \\1\end{pmatrix}}} & \text{C2a} \\{\left\lbrack {{Numerical}\quad {Formula}\quad 8} \right\rbrack \quad} & \quad \\{S_{21}^{*} = {\begin{pmatrix}b_{1} & b_{2} & b_{3} & b_{4} & b_{5} & b_{6} & b_{7} & b_{8} & b_{9} & b_{10} & b_{11} & b_{12} & b_{13} & b_{14} & b_{0}\end{pmatrix}\begin{pmatrix}S_{11}^{M} \\S_{21}^{M} \\S_{12}^{M} \\S_{22}^{M} \\\left( S_{11}^{M} \right)^{2} \\\left( S_{21}^{M} \right)^{2} \\\left( S_{12}^{M} \right)^{2} \\\left( S_{22}^{M} \right)^{2} \\{S_{11}^{M}S_{21}^{M}} \\{S_{11}^{M}S_{12}^{M}} \\{S_{11}^{M}S_{22}^{M}} \\{S_{21}^{M}S_{12}^{M}} \\{S_{21}^{M}S_{22}^{M}} \\{S_{12}^{M}S_{22}^{M}} \\1\end{pmatrix}}} & \text{C2b} \\{\left\lbrack {{Numerical}\quad {Formula}\quad 9} \right\rbrack \quad} & \quad \\{S_{12}^{*} = {\begin{pmatrix}c_{1} & c_{2} & c_{3} & c_{4} & c_{5} & c_{6} & c_{7} & c_{8} & c_{9} & c_{10} & c_{11} & c_{12} & c_{13} & c_{14} & c_{0}\end{pmatrix}\begin{pmatrix}S_{11}^{M} \\S_{21}^{M} \\S_{12}^{M} \\S_{22}^{M} \\\left( S_{11}^{M} \right)^{2} \\\left( S_{21}^{M} \right)^{2} \\\left( S_{12}^{M} \right)^{2} \\\left( S_{22}^{M} \right)^{2} \\{S_{11}^{M}S_{21}^{M}} \\{S_{11}^{M}S_{12}^{M}} \\{S_{11}^{M}S_{22}^{M}} \\{S_{21}^{M}S_{12}^{M}} \\{S_{21}^{M}S_{22}^{M}} \\{S_{12}^{M}S_{22}^{M}} \\1\end{pmatrix}}} & \text{C2c} \\{\left\lbrack {{Numerical}\quad {Formula}\quad 10} \right\rbrack \quad} & \quad \\{S_{22}^{*} = {\begin{pmatrix}d_{1} & d_{2} & d_{3} & d_{4} & d_{5} & d_{6} & d_{7} & d_{8} & d_{9} & d_{10} & d_{11} & d_{12} & d_{13} & d_{14} & d_{0}\end{pmatrix}\begin{pmatrix}S_{11}^{M} \\S_{21}^{M} \\S_{12}^{M} \\S_{22}^{M} \\\left( S_{11}^{M} \right)^{2} \\\left( S_{21}^{M} \right)^{2} \\\left( S_{12}^{M} \right)^{2} \\\left( S_{22}^{M} \right)^{2} \\{S_{11}^{M}S_{21}^{M}} \\{S_{11}^{M}S_{12}^{M}} \\{S_{11}^{M}S_{22}^{M}} \\{S_{21}^{M}S_{12}^{M}} \\{S_{21}^{M}S_{22}^{M}} \\{S_{12}^{M}S_{22}^{M}} \\1\end{pmatrix}}} & \text{C2d}\end{matrix}$

S₁₁*, S₂₁*, S₁₂*, and S_(22*): the S parameter of the target electroniccomponent 11A assumed to be obtained by the reference measuring system 1S₁₁ ^(M), S₂₁ ^(M), S₁₂ ^(M), and S₂₂ ^(M): the S parameter of thetarget electronic component 11A measured by the actual measuring system2

The interrelation equation computing means 24 determines theundetermined coefficients (a_(q), b_(q), c_(q), and d_(q): q; integersof 0 to 14) by substituting the measured results ((S₁₁ ^(p), S₂₁ ^(p),S₁₂ ^(p), and S₂₂ ^(p): p: natural numbers of 1 to 15) in theundetermined-coefficient computing equations (C1a) to (C1d).

The interrelation equation computing means 24 determines theinterrelating formulas between the results measured by the actualmeasuring system 2 and the results measured by the reference measuringsystem 1 by inserting the identified undetermined coefficients (a_(q),b_(q), c_(q), and d_(q)) into the interrelating formulas (C2a) to (C2d).The interrelating formulas are determined for each frequency point. Thedetermined interrelation equation is input and recorded in the memory 23by the interrelating formula computing means 24 via the control unitbody 22.

After the preliminary process described above, electricalcharacteristics of the target electronic component 11A are measured bythe actual measuring system 2. The measured results (electricalcharacteristics) of the target electronic component 11A in the actualmeasuring system 2 are corrected to the electrical characteristicsassumed to be obtained by the reference measuring system 1 bysubstituting the measured electrical characteristics (S parameter) inthe interrelating formulas (C2a) to (C2d).

The third embodiment having the same advantage as in the secondembodiment further produces the following advantage. That is, even ifthe actual measuring system 2 includes more complicated errors, thecorrection is performed in high accuracy. This results from the abilityof expressing complicated correlation because each point in twofour-dimensional spaces has one-to-one correspondence with a quadraticexpression according to the embodiment.

According to the second embodiment, the relative correction method usinga linear expression is incorporated in the present invention whileaccording to the third embodiment, the relative correction method usinga quadratic approximate expression is incorporated in the presentinvention. However, the present invention is not limited to theseembodiments and a relative correction method using an expression ofarbitrary degree n can be of course incorporated in the presentinvention. The higher the degree of an expression, although thecomputing time increases because of a complicated configuration, themore correction accuracy is improved.

Moreover, without using an approximate expression of arbitrary degree n,some terms of the equation may be arbitrarily omitted to the extent ofallowable reduction in accuracy. For example, when S₂₁≈S₁₂, omitting aterm including S₂₁ or S₁₂ does scarcely affect assumption accuracy. Inan electronic component being nondirectional in a signal transmissiondirection, S₂₁=S₁₂. In such a manner, the number of the correction-dataacquisition samples is reduced.

Even if a sample has symmetrical electrical characteristics, slightlydifferent values may be measured because of measurement errors.Therefore, an average value of S₂₁ and S₁₂ may be preferably used.

The correction equations simplified in such a manner become thefollowing equation (D1) and equation (D2). The equation (D1) correspondsto the equation (B1a) and equation (C1a) mentioned above. In theequations (B1b) to (B1d) and equations (C1b) to (C1d), simplifying issimilar, so that description thereof is omitted. The equation (D2)corresponds to the equation (B2) and equations (C2a) to (C2d) mentionedabove. Undetermined coefficient S_(A) ^(nM) in the equations (D1) and(D2) indicates an average value of S₂₁ ^(nM) and S₁₂ ^(nM) (n: naturalnumbers of 1 to 5). $\begin{matrix}{\left\lbrack {\text{Numerical}\quad \text{Formula}\quad 29} \right\rbrack {\begin{pmatrix}S_{11}^{1^{*}} \\S_{11}^{2^{*}} \\S^{3_{11}^{*}} \\S^{4_{11}^{*}}\end{pmatrix} = {\begin{pmatrix}S_{11}^{1M} & S_{A}^{1M} & S_{22}^{1M} & 1 \\S_{11}^{2M} & S_{A}^{2M} & S_{22}^{2M} & 1 \\S_{11}^{3M} & S_{A}^{3M} & S^{3M} & 1 \\S_{11}^{4M} & S_{A}^{4M} & S_{22}^{4M} & 1\end{pmatrix}\begin{pmatrix}a_{1} \\a_{2} \\a_{3} \\a_{0}\end{pmatrix}}}} & \text{D1} \\{\left\lbrack {\text{Numerical}\quad \text{Formula}\quad 30} \right\rbrack {S_{11}^{*} = {\left( {a_{1}\quad a_{2}a_{3}a_{0}} \right)\begin{pmatrix}S_{11}^{M} \\S_{A}^{M} \\S_{22}^{M} \\1\end{pmatrix}}}} & \text{D2}\end{matrix}$

FIG. 13 shows data corrected by the measurement error correction methodaccording to the second embodiment from the result measured by theactual measuring system 2; FIG. 14 shows data corrected by themeasurement error correction method according to the third embodimentfrom the result measured by the actual measuring system 2. From thesedata, it is confirmed that the value corrected by the measurement errorcorrection method according to the present invention approaches the truevalue of electrical characteristics of the electronic component.

FIGS. 15 and 16 are graphs showing the relationship between thecorrected result of the scattering coefficient S₂₁, which is one of Sparameter, and the actual measured result of S₂₁. FIG. 15 shows therelationship between the result corrected by the correction methodaccording to the second embodiment and the actual measured result; FIG.16 shows the relationship between the result corrected by the correctionmethod according to the third embodiment and the actual measured result.

As shown in FIGS. 15 and 16, it is understood that the result correctedby the correction method according to the second embodiment using thelinear expression substantially agrees with the actual measured result;the result corrected by the correction method according to the thirdembodiment using the quadric expression agrees with the actual measuredresult more precisely.

The measurement error correction method according to the first to thirdembodiments may be preferably incorporated in the following qualitychecking method of electronic components.

The required characteristics set for a target electronic component maybe characteristics measured by the reference measuring system. Inquality checking such an electronic component based on the resultmeasured by the actual measuring system, which does not agree with thereference measuring system, it is difficult to improve checkingaccuracy.

In applying the measurement error correction method according to thefirst to third embodiments to such a quality checking method ofelectronic components, checking result with high accuracy can beachieved.

Specifically, the electric characteristics of a target electroniccomponent measured by the actual measuring system are corrected by themeasurement error correction method according to the first to thirdembodiments, and then, by comparing between the corrected electriccharacteristics and the required characteristics, the quality of thetarget electronic component is determined. By doing so, the correctedelectric characteristics are directly comparative with the requiredcharacteristics, improving accuracy of the quality checking of a targetelectronic component.

What is claimed:
 1. A measurement-error correction method, in whichafter electrical characteristics of a target electronic component aremeasured by an actual measuring system with measured results that do notagree with a reference measuring system, the measured values arecorrected to electrical characteristics assumed to be obtained by thereference measuring system, the measurement-error correction methodcomprising the steps of: preparing a correction-data acquisition samplein advance, which generates the same electrical characteristics asarbitrary electrical characteristics of the target electronic component;measuring electrical characteristics of the correction-data acquisitionsample by the reference measuring system and the actual measuringsystem, respectively; obtaining an interrelating formula between resultsmeasured by the reference measuring system and results measured by theactual measuring system; and correcting electrical characteristics ofthe target electronic component to electrical characteristics assumed tobe obtained by the reference measuring system by substituting theelectrical characteristics of the target electronic component measuredby the actual measuring system in the interrelating formula forcomputation.
 2. A method according to claim 1, wherein the step ofobtaining the interrelating formula comprises: creating a theoreticalequation for obtaining a measurement true value of the actual measuringsystem in the signal transfer pattern and a theoretical equation forobtaining a measurement true value of the reference measuring system inthe signal transfer pattern, respectively; creating the interrelatingformula comprising an arithmetic expression, which includes anundetermined coefficient and directly and exclusively shows therelationship between the measurement true value of the actual measuringsystem and the measurement true value of the reference measuring system,based on both the theoretical equations; measuring electricalcharacteristics of the correction-data acquisition sample by thereference measuring system and the actual measuring system,respectively; and identifying the undetermined coefficient bysubstituting the electrical characteristics of the correction-dataacquisition sample measured by both the measuring systems in theinterrelating formula.
 3. A method according to claim 2, wherein aplurality of samples having electrical characteristics which aredifferent from each other as measured by the measuring system are usedas the correction-data acquisition sample.
 4. A method according toclaim 3, wherein the electrical characteristics which of the targetelectronic component are S parameter characteristics, and wherein thestep of measuring includes measuring with a network analyzer.
 5. Amethod according to claim 1, wherein the step of obtaining theinterrelating formula comprises the procedures of: creating theinterrelating formula comprising an expression of degree n (n is anatural number), which includes an undetermined coefficient andapproximately shows the relationship between the value measured by theactual measuring system and the value measured by the referencemeasuring system; measuring electrical characteristics of thecorrection-data acquisition sample by the reference measuring system andthe actual measuring system, respectively; and identifying theundetermined coefficient by creating an undetermined-coefficientcomputing equation based on the interrelating formula so as tosubstitute the electrical characteristics of the correction-dataacquisition sample measured by both the measuring systems in theundetermined-coefficient computing equation.
 6. A method according toclaim 5, wherein a plurality of samples having electricalcharacteristics which are different from each as measured by themeasuring system are used as the correction-data acquisition sample. 7.A method according to claim 6, wherein the electrical characteristics ofthe target electronic component are S parameter, and wherein the step ofmeasuring includes measuring with network analyzer.
 8. A methodaccording to claim 1, wherein a plurality of samples having electricalcharacteristics which are different from each other as measured by themeasuring system are used as the correction-data acquisition sample. 9.A method according to claim 8, wherein the electrical characteristics ofthe target electronic component S parameter characteristics, and whereinthe step of measuring includes measuring with an network analyzer.
 10. Aquality checking method of electronic components, in which a targetelectronic component with required electrical characteristics to bemeasured by a reference measuring system is measured by an actualmeasuring system with measured results, which do not agree with themeasured results from the reference measuring system, the qualitychecking method comprising the steps of: correcting the electricalcharacteristics of the target electronic component measured by theactual measuring system using a measurement-error correction methodaccording to any one of claims 1 to 9; and checking quality of thetarget electronic component by comparing the corrected electricalcharacteristics with the required electrical characteristics.
 11. Ameasuring system for measuring electronic component characteristicscomprising: target electronic component measuring means for measuringelectrical characteristics of a target electronic component; storingmeans for storing electrical characteristics, which are measured by thereference measuring system, of a correction-data acquisition samplegenerating the same electrical characteristics as arbitrary electricalcharacteristics of the target electronic component; interrelatingformula computing means for computing an interrelating formula betweenthe electrical characteristics of the correction-data acquisitionsample, which are measured by the measuring means, and the electricalcharacteristics of the correction-data acquisition sample, which aremeasured by the reference measuring system and stored in the storingmeans; and correcting means for correcting the electricalcharacteristics of the target electronic component to electricalcharacteristics assumed to be obtained by the reference measuring systemby substituting the electrical characteristics of the target electroniccomponent measured by the measuring means in the interrelating formulafor computation.
 12. A measuring system according to claim 11, whereinthe interrelating formula computing means comprises: theoreticalequation creating means for creating a theoretical equation forobtaining a measurement true value of the actual measuring system in thesignal transfer pattern and creating a theoretical equation forobtaining a measurement true value of the reference measuring system inthe signal transfer pattern; interrelating formula creating means forcreating the interrelating formula comprising an arithmetic expression,which include an undetermined coefficient and directly and exclusivelyshows the relationship between the measurement true value of the actualmeasuring system and the measurement true value of the referencemeasuring system, based on both the theoretical equations; correct dataacquisition measuring means for measuring electrical characteristics ofthe correction-data acquisition sample by the reference measuring systemand the actual measuring system, respectively; and identifying means foridentifying the undetermined coefficient by substituting the electricalcharacteristics of the correction-data acquisition sample measured byboth the measuring systems in the interrelating formula.
 13. A measuringsystem according to claim 11, wherein the interrelating formulacomputing means comprises: creating means for creating the interrelatingformula comprising an expression of degree n (n is a natural number),which includes an undetermined coefficient and approximately shows therelationship between the value measured by the actual measuring systemand the value measured by the reference measuring system; correctiondata acquisition measuring means for measuring electricalcharacteristics of the correction-data acquisition sample by thereference measuring system and the actual measuring system,respectively; and identifying means for identifying the undeterminedcoefficient by substituting the electrical characteristics of thecorrection-data acquisition sample measured by the reference measuringsystem in the interrelating formula.